List of Space Groups

3次元の空間群は230種類あります。軸の交換や原点選択を考慮すると、530種類となります。以下に、この530種類の空間群の一覧を掲載します。

  • Serial No.: 全体の通し番号 (1~530)
  • ITA No.: International Tables for Crystallography, Vol. A (以下ITA) における空間群番号 (1~230)
  • Sub No.: ITA表記に対する枝番号 (1はITA表記そのまま、2以降は軸設定などが異なる)
  • Axes, Origin: 主軸/副軸の設定 あるいは 原点選択(Origin Choice)
  • Hall symbol: Hallの記法に従った空間群表記
  • Sch. symbol: Schoenfliesの記法に従った空間群表記
  • HM symbol (short): Hermann–Mauguinの記法に従った空間群表記 (省略形)
  • HM symbol (full): Hermann–Mauguinの記法に従った空間群表記 (完全形)
  • PG No.: 点群の通し番号 (1~32)
  • PG (HM): Hermann–Mauguinの記法に従った点群表記 (省略形)
  • PG (Sch.): Schoenfliesの記法に従った点群表記
  • LC No.: ラウエクラスの通し番号 (1~11)
  • LC (HM): ラウエクラス (HM記法)
  • Crystal System No.: 結晶系の通し番号 (1~7)

Triclinic 三斜晶系

Crystal System No.: 1

Laue Class: (bar{1})

Laue Class No.: 1

Serial No. ITA No. Sub No. Axes, Origin Hall symbol Sch. symbol HM symbol (short) HM symbol (full) PG No. PG (HM) PG (Sch.)
1 1 1 P 1 (C_1^1) (P 1) (P 1) 1 (1) (C_1)
2 2 1 -P 1 (C_i^1) (P bar{1}) (P bar{1}) 2 (bar{1}) (C_i)

Monoclinic 単斜晶系

Crystal System No..: 2

Laue Class: (2/m)

Laue Class No.: 2

Serial No. ITA No. Sub No. Axes, Origin Hall symbol Sch. symbol HM symbol (short) HM symbol (full) PG No. PG (HM) PG (Sch.)
3 3 1 (b) P 2y (C_2^1) (P 2 = P 1 2 1) (P 1 2 1) 3 (2) (C_2)
4 2 (c) P 2 (P 2 = P 1 1 2) (P 1 1 2)
5 3 (a) P 2x (P 2 = P 2 1 1) (P 2 1 1)
6 4 1 (b) P 2yb (C_2^2) (P 2_1 = P 1 2_1 1) (P 1 2_1 1)
7 2 (c) P 2c (P 2_1 = P 1 1 2_1) (P 1 1 2_1)
8 3 (a) P 2xa (P 2_1 = P 2_1 1 1) (P 2_1 1 1)
9 5 1 (b1) C 2y (C_2^3) (C 2 = C 1 2 1) (C 1 2 1)
10 2 (b2) A 2y (C 2 = A 1 2 1) (A 1 2 1)
11 3 (b3) I 2y (C 2 = I 1 2 1) (I 1 2 1)
12 4 (c1) A 2 (C 2 = A 1 1 2) (A 1 1 2)
13 5 (c2) B 2 (C 2 = B 1 1 2 = B 2) (B 1 1 2)
14 6 (c3) I 2 (C 2 = I 1 1 2) (I 1 1 2)
15 7 (a1) B 2x (C 2 = B 2 1 1) (B 2 1 1)
16 8 (a2) C 2x (C 2 = C 2 1 1) (C 2 1 1)
17 9 (a3) I 2x (C 2 = I 2 1 1) (I 2 1 1)
18 6 1 (b) P -2y (C_s^1) (P m = P 1 m 1) (P 1 m 1) 4 (m) (C_s)
19 2 (c) P -2 (P m = P 1 1 m) (P 1 1 m)
20 3 (a) P -2x (P m = P m 1 1) (P m 1 1)
21 7 1 (b1) P -2yc (C_s^2) (P c = P 1 c 1) (P 1 c 1)
22 2 (b2) P -2yac (P c = P 1 n 1) (P 1 n 1)
23 3 (b3) P -2ya (P c = P 1 a 1) (P 1 a 1)
24 4 (c1) P -2a (P c = P 1 1 a) (P 1 1 a)
25 5 (c2) P -2ab (P c = P 1 1 n) (P 1 1 n)
26 6 (c3) P -2b (P c = P 1 1 b = P b) (P 1 1 b)
27 7 (a1) P -2xb (P c = P b 1 1) (P b 1 1)
28 8 (a2) P -2xbc (P c = P n 1 1) (P n 1 1)
29 9 (a3) P -2xc (P c = P c 1 1) (P c 1 1)
30 8 1 (b1) C -2y (C_s^3) (C m = C 1 m 1) (C 1 m 1)
31 2 (b2) A -2y (C m = A 1 m 1) (A 1 m 1)
32 3 (b3) I -2y (C m = I 1 m 1) (I 1 m 1)
33 4 (c1) A -2 (C m = A 1 1 m) (A 1 1 m)
34 5 (c2) B -2 (C m = B 1 1 m = B m) (B 1 1 m)
35 6 (c3) I -2 (C m = I 1 1 m) (I 1 1 m)
36 7 (a1) B -2x (C m = B m 1 1) (B m 1 1)
37 8 (a2) C -2x (C m = C m 1 1) (C m 1 1)
38 9 (a3) I -2x (C m = I m 1 1) (I m 1 1)
39 9 1 (b1) C -2yc (C_s^4) (C c = C 1 c 1) (C 1 c 1)
40 2 (b2) A -2yac (C c = A 1 n 1) (A 1 n 1)
41 3 (b3) I -2ya (C c = I 1 a 1) (I 1 a 1)
42 4 (bar{b}1) A -2ya (C c = A 1 a 1) (A 1 a 1)
43 5 (bar{b}2) C -2ybc (C c = C 1 n 1) (C 1 n 1)
44 6 (bar{b}3) I -2yc (C c = I 1 c 1) (I 1 c 1)
45 7 (c1) A -2a (C c = A 1 1 a) (A 1 1 a)
46 8 (c2) B -2bc (C c = B 1 1 n) (B 1 1 n)
47 9 (c3) I -2b (C c = I 1 1 b) (I 1 1 b)
48 10 (bar{c}1) B -2b (C c = B 1 1 b = B b) (B 1 1 b)
49 11 (bar{c}2) A -2ac (C c = A 1 1 n) (A 1 1 n)
50 12 (bar{c}3) I -2a (C c = I 1 1 a) (I 1 1 a)
51 13 (a1) B -2xb (C c = B b 1 1) (B b 1 1)
52 14 (a2) C -2xbc (C c = C n 1 1) (C n 1 1)
53 15 (a3) I -2xc (C c = I c 1 1) (I c 1 1)
54 16 (bar{a}1) C -2xc (C c = C c 1 1) (C c 1 1)
55 17 (bar{a}2) B -2xbc (C c = B n 1 1) (B n 1 1)
56 18 (bar{a}3) I -2xb (C c = I b 1 1) (I b 1 1)
57 10 1 (b) -P 2y (C_{2h}^1) (P 2/m = P 1 2/m 1) (P 1 2/m 1) 5 (2/m) (C_{2h})
58 2 (c) -P 2 (P 2/m = P 1 1 2/m) (P 1 1 2/m)
59 3 (a) -P 2x (P 2/m = P 2/m 1 1) (P 2/m 1 1)
60 11 1 (b) -P 2yb (C_{2h}^2) (P 2_1/m = P 1 2_1/m 1) (P 1 2_1/m 1)
61 2 (c) -P 2c (P 2_1/m = P 1 1 2_1/m) (P 1 1 2_1/m)
62 3 (a) -P 2xa (P 2_1/m = P 2_1/m 1 1) (P 2_1/m 1 1)
63 12 1 (b1) -C 2y (C_{2h}^3) (C 2/m = C 1 2/m 1) (C 1 2/m 1)
64 2 (b2) -A 2y (C 2/m = A 1 2/m 1) (A 1 2/m 1)
65 3 (b3) -I 2y (C 2/m = I 1 2/m 1) (I 1 2/m 1)
66 4 (c1) -A 2 (C 2/m = A 1 1 2/m) (A 1 1 2/m)
67 5 (c2) -B 2 (C 2/m = B 1 1 2/m = B 2/m) (B 1 1 2/m)
68 6 (c3) -I 2 (C 2/m = I 1 1 2/m) (I 1 1 2/m)
69 7 (a1) -B 2x (C 2/m = B 2/m 1 1) (B 2/m 1 1)
70 8 (a2) -C 2x (C 2/m = C 2/m 1 1) (C 2/m 1 1)
71 9 (a3) -I 2x (C 2/m = I 2/m 1 1) (I 2/m 1 1)
72 13 1 (b1) -P 2yc (C_{2h}^4) (P 2/c = P 1 2/c 1) (P 1 2/c 1)
73 2 (b2) -P 2yac (P 2/c = P 1 2/n 1) (P 1 2/n 1)
74 3 (b3) -P 2ya (P 2/c = P 1 2/a 1) (P 1 2/a 1)
75 4 (c1) -P 2a (P 2/c = P 1 1 2/a) (P 1 1 2/a)
76 5 (c2) -P 2ab (P 2/c = P 1 1 2/n) (P 1 1 2/n)
77 6 (c3) -P 2b (P 2/c = P 1 1 2/b = P 2/b) (P 1 1 2/b)
78 7 (a1) -P 2xb (P 2/c = P 2/b 1 1) (P 2/b 1 1)
79 8 (a2) -P 2xbc (P 2/c = P 2/n 1 1) (P 2/n 1 1)
80 9 (a3) -P 2xc (P 2/c = P 2/c 1 1) (P 2/c 1 1)
81 14 1 (b1) -P 2ybc (C_{2h}^5) (P 2_1/c = P 1 2_1/c 1) (P 1 2_1/c 1)
82 2 (b2) -P 2yn (P 2_1/c = P 1 2_1/n 1) (P 1 2_1/n 1)
83 3 (b3) -P 2yab (P 2_1/c = P 1 2_1/a 1) (P 1 2_1/a 1)
84 4 (c1) -P 2ac (P 2_1/c = P 1 1 2_1/a) (P 1 1 2_1/a)
85 5 (c2) -P 2n (P 2_1/c = P 1 1 2_1/n) (P 1 1 2_1/n)
86 6 (c3) -P 2bc (P 2_1/c = P 1 1 2_1/b = P 2_1/b) (P 1 1 2_1/b)
87 7 (a1) -P 2xab (P 2_1/c = P 2_1/b 1 1) (P 2_1/b 1 1)
88 8 (a2) -P 2xn (P 2_1/c = P 2_1/n 1 1) (P 2_1/n 1 1)
89 9 (a3) -P 2xac (P 2_1/c = P 2_1/c 1 1) (P 2_1/c 1 1)
90 15 1 (b1) -C 2yc (C_{2h}^6) (C 2/c = C 1 2/c 1) (C 1 2/c 1)
91 2 (b2) -A 2yac (C 2/c = A 1 2/n 1) (A 1 2/n 1)
92 3 (b3) -I 2ya (C 2/c = I 1 2/a 1) (I 1 2/a 1)
93 4 (bar{b}1) -A 2ya (C 2/c = A 1 2/a 1) (A 1 2/a 1)
94 5 (bar{b}2) -C 2ybc (C 2/c = C 1 2/n 1) (C 1 2/n 1)
95 6 (bar{b}3) -I 2yc (C 2/c = I 1 2/c 1) (I 1 2/c 1)
96 7 (c1) -A 2a (C 2/c = A 1 1 2/a) (A 1 1 2/a)
97 8 (c2) -B 2bc (C 2/c = B 1 1 2/n) (B 1 1 2/n)
98 9 (c3) -I 2b (C 2/c = I 1 1 2/b) (I 1 1 2/b)
99 10 (bar{c}1) -B 2b (C 2/c = B 1 1 2/b = B 2/b) (B 1 1 2/b)
100 11 (bar{c}2) -A 2ac (C 2/c = A 1 1 2/n) (A 1 1 2/n)
101 12 (bar{c}3) -I 2a (C 2/c = I 1 1 2/a) (I 1 1 2/a)
102 13 (a1) -B 2xb (C 2/c = B 2/b 1 1) (B 2/b 1 1)
103 14 (a2) -C 2xbc (C 2/c = C 2/n 1 1) (C 2/n 1 1)
104 15 (a3) -I 2xc (C 2/c = I 2/c 1 1) (I 2/c 1 1)
105 16 (bar{a}1) -C 2xc (C 2/c = C 2/c 1 1) (C 2/c 1 1)
106 17 (bar{a}2) -B 2xbc (C 2/c = B 2/n 1 1) (B 2/n 1 1)
107 18 (bar{a}3) -I 2xb (C 2/c = I 2/b 1 1) (I 2/b 1 1)

Orthorhombic 直方晶系

Crystal System No.: 3

Laue Class: (mmm)

Laue Class No.: 2

注: HM symbolが 2つ書かれている空間群があります (ITA Nos. 39, 41, 64, 67)。上段がITA 4thまでの表記で、後段が5th以降の表記です。

Serial No. ITA No. Sub No. Axes, Origin Hall symbol Sch symbol HM symbol (short) HM symbol (full) PG No. PG (HM) PG (Sch.)
108 16 1 P 2 2 (D_2^1) (P 2 2 2) (P 2 2 2) 6 (2 2 2) (D_2)
109 17 1 P 2c 2 (D_2^2) (P 2 2 2_1) (P 2 2 2_1)
110 2 (cab) P 2a 2a (P 2_1 2 2) (P 2_1 2 2)
111 3 (bca) P 2 2b (P 2 2_1 2) (P 2 2_1 2)
112 18 1 P 2 2ab (D_2^3) (P 2_1 2_1 2) (P 2_1 2_1 2)
113 2 (cab) P 2bc 2 (P 2 2_1 2_1) (P 2 2_1 2_1)
114 3 (bca) P 2ac 2ac (P 2_1 2 2_1) (P 2_1 2 2_1)
115 19 1 P 2ac 2ab (D_2^4) (P 2_1 2_1 2_1) (P 2_1 2_1 2_1)
116 20 1 C 2c 2 (D_2^5) (C 2 2 2_1) (C 2 2 2_1)
117 2 (cab) A 2a 2a (A 2_1 2 2) (A 2_1 2 2)
118 3 (bca) B 2 2b (B 2 2_1 2) (B 2 2_1 2)
119 21 1 C 2 2 (D_2^6) (C 2 2 2) (C 2 2 2)
120 2 (cab) A 2 2 (A 2 2 2) (A 2 2 2)
121 3 (bca) B 2 2 (B 2 2 2) (B 2 2 2)
122 22 1 F 2 2 (D_2^7) (F 2 2 2) (F 2 2 2)
123 23 1 I 2 2 (D_2^8) (I 2 2 2) (I 2 2 2)
124 24 1 I 2b 2c (D_2^9) (I 2_1 2_1 2_1) (I 2_1 2_1 2_1)
125 25 1 P 2 -2 (C_{2v}^1) (P m m 2) (P m m 2) 7 (m m 2) (C_{2v})
126 2 (cab) P -2 2 (P 2 m m) (P 2 m m)
127 3 (bca) P -2 -2 (P m 2 m) (P m 2 m)
128 26 1 P 2c -2 (C_{2v}^2) (P m c 2_1) (P m c 2_1)
129 2 (babar{c}) P 2c -2c (P c m 2_1) (P c m 2_1)
130 3 (cab) P -2a 2a (P 2_1 m a) (P 2_1 m a)
131 4 (bar{c}ba) P -2 2a (P 2_1 a m) (P 2_1 a m)
132 5 (bca) P -2 -2b (P b 2_1 m) (P b 2_1 m)
133 6 (abar{c}b) P -2b -2 (P m 2_1 b) (P m 2_1 b)
134 27 1 P 2 -2c (C_{2v}^3) (P c c 2) (P c c 2)
135 2 (cab) P -2a 2 (P 2 a a) (P 2 a a)
136 3 (bca) P -2b -2b (P b 2 b) (P b 2 b)
137 28 1 P 2 -2a (C_{2v}^4) (P m a 2) (P m a 2)
138 2 (babar{c}) P 2 -2b (P b m 2) (P b m 2)
139 3 (cab) P -2b 2 (P 2 m b) (P 2 m b)
140 4 (bar{c}ba) P -2c 2 (P 2 c m) (P 2 c m)
141 5 (bca) P -2c -2c (P c 2 m) (P c 2 m)
142 6 (abar{c}b) P -2a -2a (P m 2 a) (P m 2 a)
143 29 1 P 2c -2ac (C_{2v}^5) (P c a 2_1) (P c a 2_1)
144 2 (babar{c}) P 2c -2b (P b c 2_1) (P b c 2_1)
145 3 (cab) P -2b 2a (P 2_1 a b) (P 2_1 a b)
146 4 (bar{c}ba) P -2ac 2a (P 2_1 c a) (P 2_1 c a)
147 5 (bca) P -2bc -2c (P c 2_1 b) (P c 2_1 b)
148 6 (abar{c}b) P -2a -2ab (P b 2_1 a) (P b 2_1 a)
149 30 1 P 2 -2bc (C_{2v}^6) (P n c 2) (P n c 2)
150 2 (babar{c}) P 2 -2ac (P c n 2) (P c n 2)
151 3 (cab) P -2ac 2 (P 2 n a) (P 2 n a)
152 4 (bar{c}ba) P -2ab 2 (P 2 a n) (P 2 a n)
153 5 (bca) P -2ab -2ab (P b 2 n) (P b 2 n)
154 6 (abar{c}b) P -2bc -2bc (P n 2 b) (P n 2 b)
155 31 1 P 2ac -2 (C_{2v}^7) (P m n 2_1) (P m n 2_1)
156 2 (babar{c}) P 2bc -2bc (P n m 2_1) (P n m 2_1)
157 3 (cab) P -2ab 2ab (P 2_1 m n) (P 2_1 m n)
158 4 (bar{c}ba) P -2 2ac (P 2_1 n m) (P 2_1 n m)
159 5 (bca) P -2 -2bc (P n 2_1 m) (P n 2_1 m)
160 6 (abar{c}b) P -2ab -2 (P m 2_1 n) (P m 2_1 n)
161 32 1 P 2 -2ab (C_{2v}^8) (P b a 2) (P b a 2)
162 2 (cab) P -2bc 2 (P 2 c b) (P 2 c b)
163 3 (bca) P -2ac -2ac (P c 2 a) (P c 2 a)
164 33 1 P 2c -2n (C_{2v}^9) (P n a 2_1) (P n a 2_1)
165 2 (babar{c}) P 2c -2ab (P b n 2_1) (P b n 2_1)
166 3 (cab) P -2bc 2a (P 2_1 n b) (P 2_1 n b)
167 4 (bar{c}ba) P -2n 2a (P 2_1 c n) (P 2_1 c n)
168 5 (bca) P -2n -2ac (P c 2_1 n) (P c 2_1 n)
169 6 (abar{c}b) P -2ac -2n (P n 2_1 a) (P n 2_1 a)
170 34 1 P 2 -2n (C_{2v}^{10}) (P n n 2) (P n n 2)
171 2 (cab) P -2n 2 (P 2 n n) (P 2 n n)
172 3 (bca) P -2n -2n (P n 2 n) (P n 2 n)
173 35 1 C 2 -2 (C_{2v}^{11}) (C m m 2) (C m m 2)
174 2 (cab) A -2 2 (A 2 m m) (A 2 m m)
175 3 (bca) B -2 -2 (B m 2 m) (B m 2 m)
176 36 1 C 2c -2 (C_{2v}^{12}) (C m c 2_1) (C m c 2_1)
177 2 (babar{c}) C 2c -2c (C c m 2_1) (C c m 2_1)
178 3 (cab) A -2a 2a (A 2_1 m a) (A 2_1 m a)
179 4 (bar{c}ba) A -2 2a (A 2_1 a m) (A 2_1 a m)
180 5 (bca) B -2 -2b (B b 2_1 m) (B b 2_1 m)
181 6 (abar{c}b) B -2b -2 (B m 2_1 b) (B m 2_1 b)
182 37 1 C 2 -2c (C_{2v}^{13}) (C c c 2) (C c c 2)
183 2 (cab) A -2a 2 (A 2 a a) (A 2 a a)
184 3 (bca) B -2b -2b (B b 2 b) (B b 2 b)
185 38 1 A 2 -2 (C_{2v}^{14}) (A m m 2) (A m m 2)
186 2 (babar{c}) B 2 -2 (B m m 2) (B m m 2)
187 3 (cab) B -2 2 (B 2 m m) (B 2 m m)
188 4 (bar{c}ba) C -2 2 (C 2 m m) (C 2 m m)
189 5 (bca) C -2 -2 (C m 2 m) (C m 2 m)
190 6 (abar{c}b) A -2 -2 (A m 2 m) (A m 2 m)
191 39 1 A 2 -2c (C_{2v}^{15}) (A b m 2)
(A e m 2)
(A b m 2)
(A e m 2)
192 2 (babar{c}) B 2 -2c (B m a 2)
(B m e 2)
(B m a 2)
(B m e 2)
193 3 (cab) B -2c 2 (B 2 c m)
(B 2 e m)
(B 2 c m)
(B 2 e m)
194 4 (bar{c}ba) C -2b 2 (C 2 m b)
(C 2 m e)
(C 2 m b)
(C 2 m e)
195 5 (bca) C -2b -2b (C m 2 a)
(C m 2 e)
(C m 2 a)
(C m 2 e)
196 6 (abar{c}b) A -2c -2c (A c 2 m)
(A e 2 m)
(A c 2 m)
(A e 2 m)
197 40 1 A 2 -2a (C_{2v}^{16}) (A m a 2) (A m a 2)
198 2 (babar{c}) B 2 -2b (B b m 2) (B b m 2)
199 3 (cab) B -2b 2 (B 2 m b) (B 2 m b)
200 4 (bar{c}ba) C -2c 2 (C 2 c m) (C 2 c m)
201 5 (bca) C -2c -2c (C c 2 m) (C c 2 m)
202 6 (abar{c}b) A -2a -2a (A m 2 a) (A m 2 a)
203 41 1 A 2 -2ac (C_{2v}^{17}) (A b a 2)
(A e a 2)
(A b a 2)
(A e a 2)
204 2 (babar{c}) B 2 -2bc (B b a 2)
(B b e 2 )
(B b a 2)
(B b e 2 )
205 3 (cab) B -2bc 2 (B 2 c b)
(B 2 e b)
(B 2 c b)
(B 2 e b)
206 4 (bar{c}ba) C -2bc 2 (C 2 c b)
(C 2 c e)
(C 2 c b)
(C 2 c e)
207 5 (bca) C -2bc -2bc (C c 2 a)
(C c 2 e)
(C c 2 a)
(C c 2 e)
208 6 (abar{c}b) A -2ac -2ac (A c 2 a)
(A e 2 a)
(A c 2 a)
(A e 2 a)
209 42 1 F 2 -2 (C_{2v}^{18}) (F m m 2) (F m m 2)
210 2 (cab) F -2 2 (F 2 m m) (F 2 m m)
211 3 (bca) F -2 -2 (F m 2 m) (F m 2 m)
212 43 1 F 2 -2d (C_{2v}^{19}) (F d d 2) (F d d 2)
213 2 (cab) F -2d 2 (F 2 d d) (F 2 d d)
214 3 (bca) F -2d -2d (F d 2 d) (F d 2 d)
215 44 1 I 2 -2 (C_{2v}^{20}) (I m m 2) (I m m 2)
216 2 (cab) I -2 2 (I 2 m m) (I 2 m m)
217 3 (bca) I -2 -2 (I m 2 m) (I m 2 m)
218 45 1 I 2 -2c (C_{2v}^{21}) (I b a 2) (I b a 2)
219 2 (cab) I -2a 2 (I 2 c b) (I 2 c b)
220 3 (bca) I -2b -2b (I c 2 a) (I c 2 a)
221 46 1 I 2 -2a (C_{2v}^{22}) (I m a 2) (I m a 2)
222 2 (babar{c}) I 2 -2b (I b m 2) (I b m 2)
223 3 (cab) I -2b 2 (I 2 m b) (I 2 m b)
224 4 (bar{c}ba) I -2c 2 (I 2 c m) (I 2 c m)
225 5 (bca) I -2c -2c (I c 2 m) (I c 2 m)
226 6 (abar{c}b) I -2a -2a (I m 2 a) (I m 2 a)
227 47 1 -P 2 2 (D_{2h}^1) (P m m m) (P 2/m 2/m 2/m) 8 (m m m) (D_{2h})
228 48 1 (1) P 2 2 -1n (D_{2h}^2) (P n n n) (P 2/n 2/n 2/n)
229 2 (2) -P 2ab 2bc
230 49 1 -P 2 2c (D_{2h}^3) (P c c m) (P 2/c 2/c 2/m)
231 2 (cab) -P 2a 2 (P m a a) (P 2/m 2/a 2/a)
232 3 (bca) -P 2b 2b (P b m b) (P 2/b 2/m 2/b)
233 50 1 (1) P 2 2 -1ab (D_{2h}^4) (P b a n) (P 2/b 2/a 2/n)
234 2 (2) -P 2ab 2b
235 3 (1cab) P 2 2 -1bc (P n c b) (P 2/n 2/c 2/b)
236 4 (2cab) -P 2b 2bc
237 5 (1bca) P 2 2 -1ac (P c n a) (P 2/c 2/n 2/a)
238 6 (2bca) -P 2a 2c
239 51 1 -P 2a 2a (D_{2h}^5) (P m m a) (P 2_1/m 2/m 2/a)
240 2 (babar{c}) -P 2b 2 (P m m b) (P 2/m 2_1/m 2/b)
241 3 (cab) -P 2 2b (P b m m) (P 2/b 2_1/m 2/m)
242 4 (bar{c}ba) -P 2c 2c (P c m m) (P 2/c 2/m 2_1/m)
243 5 (bca) -P 2c 2 (P m c m) (P 2/m 2/c 2_1/m)
244 6 (abar{c}b) -P 2 2a (P m a m) (P 2_1/m 2/a 2/m)
245 52 1 -P 2a 2bc (D_{2h}^6) (P n n a) (P 2/n 2_1/n 2/a)
246 2 (babar{c}) -P 2b 2n (P n n b) (P 2_1/n 2/n 2/b)
247 3 (cab) -P 2n 2b (P b n n) (P 2/b 2/n 2_1/n)
248 4 (bar{c}ba) -P 2ab 2c (P c n n) (P 2/c 2_1/n 2/n)
249 5 (bca) -P 2ab 2n (P n c n) (P 2_1/n 2/c 2/n)
250 6 (abar{c}b) -P 2n 2bc (P n a n) (P 2/n 2/a 2_1/n)
251 53 1 -P 2ac 2 (D_{2h}^7) (P m n a) (P 2/m 2/n 2_1/a)
252 2 (babar{c}) -P 2bc 2bc (P n m b) (P 2/n 2/m 2_1/b)
253 3 (cab) -P 2ab 2ab (P b m n) (P 2_1/b 2/m 2/n)
254 4 (bar{c}ba) -P 2 2ac (P c n m) (P 2_1/c 2/n 2/m)
255 5 (bca) -P 2 2bc (P n c m) (P 2/n 2_1/c 2/m)
256 6 (abar{c}b) -P 2ab 2 (P m a n) (P 2/m 2_1/a 2/n)
257 54 1 -P 2a 2ac (D_{2h}^8) (P c c a) (P 2_1/c 2/c 2/a)
258 2 (babar{c}) -P 2b 2c (P c c b) (P 2/c 2_1/c 2/b)
259 3 (cab) -P 2a 2b (P b a a) (P 2/b 2_1/a 2/a)
260 4 (bar{c}ba) -P 2ac 2c (P c a a) (P 2/c 2/a 2_1/a)
261 5 (bca) -P 2bc 2b (P b c b) (P 2/b 2/c 2_1/b)
262 6 (abar{c}b) -P 2b 2ab (P b a b) (P 2_1/b 2/a 2/b)
263 55 1 -P 2 2ab (D_{2h}^9) (P b a m) (P 2_1/b 2_1/a 2/m)
264 2 (cab) -P 2bc 2 (P m c b) (P 2/m 2_1/c 2_1/b)
265 3 (bca) -P 2ac 2ac (P c m a) (P 2_1/c 2/m 2_1/a)
266 56 1 -P 2ab 2ac (D_{2h}^{10}) (P c c n) (P 2_1/c 2_1/c 2/n)
267 2 (cab) -P 2ac 2bc (P n a a) (P 2/n 2_1/a 2_1/a)
268 3 (bca) -P 2bc 2ab (P b n b) (P 2_1/b 2/n 2_1/b)
269 57 1 -P 2c 2b (D_{2h}^{11}) (P b c m) (P 2/b 2_1/c 2_1/m)
270 2 (babar{c}) -P 2c 2ac (P c a m) (P 2_1/c 2/a 2_1/m)
271 3 (cab) -P 2ac 2a (P m c a) (P 2_1/m 2/c 2_1/a)
272 4 (bar{c}ba) -P 2b 2a (P m a b) (P 2_1/m 2_1/a 2/b)
273 5 (bca) -P 2a 2ab (P b m a) (P 2_1/b 2_1/m 2/a)
274 6 (abar{c}b) -P 2bc 2c (P c m b) (P 2/c 2_1/m 2_1/b)
275 58 1 -P 2 2n (D_{2h}^{12}) (P n n m) (P 2_1/n 2_1/n 2/m)
276 2 (cab) -P 2n 2 (P m n n) (P 2/m 2_1/n 2_1/n)
277 3 (bca) -P 2n 2n (P n m n) (P 2_1/n 2/m 2_1/n)
278 59 1 (1) P 2 2ab -1ab (D_{2h}^{13}) (P m m n) (P 2_1/m 2_1/m 2/n)
279 2 (2) -P 2ab 2a
280 3 (1cab) P 2bc 2 -1bc (P n m m) (P 2/n 2_1/m 2_1/m)
281 4 (2cab) -P 2c 2bc
282 5 (1bca) P 2ac 2ac -1ac (P m n m) (P 2_1/m 2/n 2_1/m)
283 6 (2bca) -P 2c 2a
284 60 1 -P 2n 2ab (D_{2h}^{14}) (P b c n) (P 2_1/b 2/c 2_1/n)
285 2 (babar{c}) -P 2n 2c (P c a n) (P 2/c 2_1/a 2_1/n)
286 3 (cab) -P 2a 2n (P n c a) (P 2_1/n 2_1/c 2/a)
287 4 (bar{c}ba) -P 2bc 2n (P n a b) (P 2_1/n 2/a 2_1/b)
288 5 (bca) -P 2ac 2b (P b n a) (P 2/b 2_1/n 2_1/a)
289 6 (abar{c}b) -P 2b 2ac (P c n b) (P 2_1/c 2_1/n 2/b)
290 61 1 -P 2ac 2ab (D_{2h}^{15}) (P b c a) (P 2_1/b 2_1/c 2_1/a)
291 2 (babar{c}) -P 2bc 2ac (P c a b) (P 2_1/c 2_1/a 2_1/b)
292 62 1 -P 2ac 2n (D_{2h}^{16}) (P n m a) (P 2_1/n 2_1/m 2_1/a)
293 2 (babar{c}) -P 2bc 2a (P m n b) (P 2_1/m 2_1/n 2_1/b)
294 3 (cab) -P 2c 2ab (P b n m) (P 2_1/b 2_1/n 2_1/m)
295 4 (bar{c}ba) -P 2n 2ac (P c m n) (P 2_1/c 2_1/m 2_1/n)
296 5 (bca) -P 2n 2a (P m c n) (P 2_1/m 2_1/c 2_1/n)
297 6 (abar{c}b) -P 2c 2n (P n a m) (P 2_1/n 2_1/a 2_1/m)
298 63 1 -C 2c 2 (D_{2h}^{17}) (C m c m) (C 2/m 2/c 2_1/m)
299 2 (babar{c}) -C 2c 2c (C c m m) (C 2/c 2/m 2_1/m)
300 3 (cab) -A 2a 2a (A m m a) (A 2_1/m 2/m 2/a)
301 4 (bar{c}ba) -A 2 2a (A m a m) (A 2_1/m 2/a 2/m)
302 5 (bca) -B 2 2b (B b m m) (B 2/b 2_1/m 2/m)
303 6 (abar{c}b) -B 2b 2 (B m m b) (B 2/m 2_1/m 2/b)
304 64 1 -C 2bc 2 (D_{2h}^{18}) (C m c a)
(C m c e)
(C 2/m 2/c 2_1/a)
(C 2/m 2/c 2_1/e)
305 2 (babar{c}) -C 2bc 2bc (C c m b)
(C c m e)
(C 2/c 2/m 2_1/b)
(C 2/c 2/m 2_1/e)
306 3 (cab) -A 2ac 2ac (A b m a)
(A e m a)
(A 2_1/b 2/m a)
(A 2_1/e 2/m a)
307 4 (bar{c}ba) -A 2 2ac (A c a m)
(A e a m)
(A 2_1/c 2/a 2/m)
(A 2_1/e 2/a 2/m)
308 5 (bca) -B 2 2bc (B b c m)
(B b e m)
(B 2/b 2_1/c 2/m)
(B 2/b 2_1/e 2/m)
309 6 (abar{c}b) -B 2bc 2 (B m a b)
(B m e b)
(B 2/m 2_1/a 2/b)
(B 2/m 2_1/e 2/b)
310 65 1 -C 2 2 (D_{2h}^{19}) (C m m m) (C 2/m 2/m 2/m)
311 2 (cab) -A 2 2 (A m m m) (A 2/m 2/m 2/m)
312 3 (bca) -B 2 2 (B m m m) (B 2/m 2/m 2/m)
313 66 1 -C 2 2c (D_{2h}^{20}) (C c c m) (C 2/c 2/c 2/m)
314 2 (cab) -A 2a 2 (A m a a) (A 2/m 2/a 2/a)
315 3 (bca) -B 2b 2b (B b m b) (B 2/b 2/m 2/b)
316 67 1 -C 2b 2 (D_{2h}^{21}) (C m m a)
(C m m e)
(C 2/m 2/m 2/a)
(C 2/m 2/m 2/e)
317 2 (babar{c}) -C 2b 2b (C m m b)
(C m m e)
(C 2/m 2/m 2/b)
(C 2/m 2/m 2/e)
318 3 (cab) -A 2c 2c (A b m m)
(A e m m)
(A 2/b 2/m 2/m)
(A 2/e 2/m 2/m)
319 4 (bar{c}ba) -A 2 2c (A c m m)
(A e m m)
(A 2/c 2/m 2/m)
(A 2/e 2/m 2/m)
320 5 (bca) -B 2 2c (B m c m)
(B m e m)
(B 2/m 2/c 2/m)
(B 2/m 2/e 2/m)
321 6 (abar{c}b) -B 2c 2 (B m a m)
(B m e m)
(B 2/m 2/a 2/m)
(B 2/m 2/e 2/m)
322 68 1 (1) C 2 2 -1bc (D_{2h}^{22}) (C c c a)
(C c c e)
(C 2/c 2/c 2/a)
(C 2/c 2/c 2/e)
323 2 (2) -C 2b 2bc
324 3 (1babar{c}) C 2 2 -1bc (C c c b)
(C c c e)
(C 2/c 2/c 2/b)
(C 2/c 2/c 2/e)
325 4 (2babar{c}) -C 2b 2c
326 5 (1cab) A 2 2 -1ac (A b a a)
(A e a a)
(A 2/b 2/a 2/a)
(A 2/e 2/a 2/a)
327 6 (2cab) -A 2a 2c
328 7 (1bar{c}ba) A 2 2 -1ac (A c a a)
(A e a a)
(A 2/c 2/a 2/a)
(A 2/e 2/a 2/a)
329 8 (2bar{c}ba) -A 2ac 2c
330 9 (1bca) B 2 2 -1bc (B b c b)
(B b e b)
(B 2/b 2/c 2/b)
(B 2/b 2/e 2/b)
331 10 (2bca) -B 2bc 2b
332 11 (1abar{c}b) B 2 2 -1bc (B b a b)
(B b e b)
(B 2/b 2/a 2/b)
(B 2/b 2/e 2/b)
333 12 (2abar{c}b) -B 2b 2bc
334 69 1 -F 2 2 (D_{2h}^{23}) (F m m m) (F 2/m 2/m 2/m)
335 70 1 (1) F 2 2 -1d (D_{2h}^{24}) (F d d d) (F 2/d 2/d 2/d)
336 2 (2) -F 2uv 2vw
337 71 1 -I 2 2 (D_{2h}^{25}) (I m m m) (I 2/m 2/m 2/m)
338 72 1 -I 2 2c (D_{2h}^{26}) (I b a m) (I 2/b 2/a 2/m)
339 2 (cab) -I 2a 2 (I m c b) (I 2/m 2/c 2/b)
340 3 (bca) -I 2b 2b (I c m a) (I 2/c 2/m 2/a)
341 73 1 -I 2b 2c (D_{2h}^{27}) (I b c a) (I 2/b 2/c 2/a)
342 2 (babar{c}) -I 2a 2b (I c a b) (I 2/c 2/a 2/b)
343 74 1 -I 2b 2 (D_{2h}^{28}) (I m m a) (I 2/m 2/m 2/a)
344 2 (babar{c}) -I 2a 2a (I m m b) (I 2/m 2/m 2/b)
345 3 (cab) -I 2c 2c (I b m m) (I 2/b 2/m 2/m)
346 4 (bar{c}ba) -I 2 2b (I c m m) (I 2/c 2/m 2/m)
347 5 (bca) -I 2 2a (I m c m) (I 2/m 2/c 2/m)
348 6 (abar{c}b) -I 2c 2 (I m a m) (I 2/m 2/a 2/m)

Tetragonal 正方晶系

Crystal System No.: 4

Serial No. ITA No. Sub No. Axes, Origin Hall symbol Sch. symbol HM symbol (short) HM symbol (full) PG No. PG (HM) PG (Sch.) LC No. LC (HM)
349 75 1 P 4 (C_4^1) (P 4) (P 4) 9 (4) (C_4) 4 (4/m)
350 76 1 P 4w (C_4^2) (P 4_1) (P 4_1)
351 77 1 P 4c (C_4^3) (P 4_2) (P 4_2)
352 78 1 P 4cw (C_4^4) (P 4_3) (P 4_3)
353 79 1 I 4 (C_4^5) (I 4) (I 4)
354 80 1 I 4bw (C_4^6) (I 4_1) (I 4_1)
355 81 1 P -4 (S_4^1) (P bar{4}) (P bar{4}) 10 (bar{4}) (S_4)
356 82 1 I -4 (S_4^2) (I bar{4}) (I bar{4})
357 83 1 -P 4 (C_{4h}^1) (P 4/m) (P 4/m) 11 (4/m) (C_{4h})
358 84 1 -P 4c (C_{4h}^2) (P 4_2/ m) (P 4_2/m)
359 85 1 (1) P 4ab -1ab (C_{4h}^3) (P 4/n) (P 4/n)
360 2 (2) -P 4a
361 86 1 (1) P 4n -1n (C_{4h}^4) (P 4_2/ n) (P 4_2/n)
362 2 (2) -P 4bc
363 87 1 -I 4 (C_{4h}^5) (I 4/m) (I 4/m)
364 88 1 (1) I 4bw -1bw (C_{4h}^6) (I 4_1/ a) (I 4_1/a)
365 2 (2) -I 4ad
366 89 1 P 4 2 (D_4^1) (P 4 2 2) (P 4 2 2) 12 (4 2 2) (D_4) 5 (4/mmm)
367 90 1 P 4ab 2ab (D_4^2) (P 4 2_1 2) (P 4 2_1 2)
368 91 1 P 4w 2c (D_4^3) (P 4_1 2 2) (P 4_1 2 2)
369 92 1 P 4abw 2nw (D_4^4) (P 4_1 2_1 2) (P 4_1 2_1 2)
370 93 1 P 4c 2 (D_4^5) (P 4_2 2 2) (P 4_2 2 2)
371 94 1 P 4n 2n (D_4^6) (P 4_2 2_1 2) (P 4_2 2_1 2)
372 95 1 P 4cw 2c (D_4^7) (P 4_3 2 2) (P 4_3 2 2)
373 96 1 P 4nw 2abw (D_4^8) (P 4_3 2_1 2) (P 4_3 2_1 2)
374 97 1 I 4 2 (D_4^9) (I 4 2 2) (I 4 2 2)
375 98 1 I 4bw 2bw (D_4^{10}) (I 4_1 2 2) (I 4_1 2 2)
376 99 1 P 4 -2 (C_{4v}^1) (P 4 m m) (P 4 m m) 13 (4 m m) (C_{4v})
377 100 1 P 4 -2ab (C_{4v}^2) (P 4 b m) (P 4 b m)
378 101 1 P 4c -2c (C_{4v}^3) (P 4_2 c m) (P 4_2 c m)
379 102 1 P 4n -2n (C_{4v}^4) (P 4_2 n m) (P 4_2 n m)
380 103 1 P 4 -2c (C_{4v}^5) (P 4 c c) (P 4 c c)
381 104 1 P 4 -2n (C_{4v}^6) (P 4 n c) (P 4 n c)
382 105 1 P 4c -2 (C_{4v}^7) (P 4_2 m c) (P 4_2 m c)
383 106 1 P 4c -2ab (C_{4v}^8) (P 4_2 b c) (P 4_2 b c)
384 107 1 I 4 -2 (C_{4v}^9) (I 4 m m) (I 4 m m)
385 108 1 I 4 -2c (C_{4v}^{10}) (I 4 c m) (I 4 c m)
386 109 1 I 4bw -2 (C_{4v}^{11}) (I 4_1 m d) (I 4_1 m d)
387 110 1 I 4bw -2c (C_{4v}^{12}) (I 4_1 c d) (I 4_1 c d)
388 111 1 P -4 2 (D_{2d}^1) (P bar{4} 2 m) (P bar{4} 2 m) 14 (bar{4} 2 m) (D_{2d})
389 112 1 P -4 2c (D_{2d}^2) (P bar{4} 2 c) (P bar{4} 2 c)
390 113 1 P -4 2ab (D_{2d}^3) (P bar{4} 2_1 m) (P bar{4} 2_1 m)
391 114 1 P -4 2n (D_{2d}^4) (P bar{4} 2_1 c) (P bar{4} 2_1 c)
392 115 1 P -4 -2 (D_{2d}^5) (P bar{4} m 2) (P bar{4} m 2)
393 116 1 P -4 -2c (D_{2d}^6) (P bar{4} c 2) (P bar{4} c 2)
394 117 1 P -4 -2ab (D_{2d}^7) (P bar{4} b 2) (P bar{4} b 2)
395 118 1 P -4 -2n (D_{2d}^8) (P bar{4} n 2) (P bar{4} n 2)
396 119 1 I -4 -2 (D_{2d}^9) (I bar{4} m 2) (I bar{4} m 2)
397 120 1 I -4 -2c (D_{2d}^{10}) (I bar{4} c 2) (I bar{4} c 2)
398 121 1 I -4 2 (D_{2d}^{11}) (I bar{4} 2 m) (I bar{4} 2 m)
399 122 1 I -4 2bw (D_{2d}^{12}) (I bar{4} 2 d) (I bar{4} 2 d)
400 123 1 -P 4 2 (D_{4h}^1) (P 4/m m m) (P 4/m 2/m 2/m) 15 (4/m m m) (D_{4h})
401 124 1 -P 4 2c (D_{4h}^2) (P 4/m c c) (P 4/m 2/c 2/c)
402 125 1 (1) P 4 2 -1ab (D_{4h}^3) (P 4/n b m) (P 4/n 2/b 2/m)
403 2 (2) -P 4a 2b
404 126 1 (1) P 4 2 -1n (D_{4h}^4) (P 4/n n c) (P 4/n 2/n 2/c)
405 2 (2) -P 4a 2bc
406 127 1 -P 4 2ab (D_{4h}^5) (P 4/m b m) (P 4/m 2_1/b m)
407 128 1 -P 4 2n (D_{4h}^6) (P 4/m n c) (P 4/m 2_1/n c)
408 129 1 (1) P 4ab 2ab -1ab (D_{4h}^7) (P 4/n m m) (P 4/n 2_1/m m)
409 2 (2) -P 4a 2a
410 130 1 (1) P 4ab 2n -1ab (D_{4h}^8) (P 4/n c c) (P 4/n 2_1/c c)
411 2 (2) -P 4a 2ac
412 131 1 -P 4c 2 (D_{4h}^9) (P 4_2/ m m c) (P 4_2/m 2/m 2/c)
413 132 1 -P 4c 2c (D_{4h}^{10}) (P 4_2/ m c m) (P 4_2/m 2/c 2/m)
414 133 1 (1) P 4n 2c -1n (D_{4h}^{11}) (P 4_2/ n b c) (P 4_2/n 2/b 2/c)
415 2 (2) -P 4ac 2b
416 134 1 (1) P 4n 2 -1n (D_{4h}^{12}) (P 4_2/ n n m) (P 4_2/n 2/n 2/m)
417 2 (2) -P 4ac 2bc
418 135 1 -P 4c 2ab (D_{4h}^{13}) (P 4_2/ m b c) (P 4_2/m 2_1/b 2/c)
419 136 1 -P 4n 2n (D_{4h}^{14}) (P 4_2/ m n m) (P 4_2/m 2_1/n 2/m)
420 137 1 (1) P 4n 2n -1n (D_{4h}^{15}) (P 4_2/ n m c) (P 4_2/n 2_1/m 2/c)
421 2 (2) -P 4ac 2a
422 138 1 (1) P 4n 2ab -1n (D_{4h}^{16}) (P 4_2/ n c m) (P 4_2/n 2_1/c 2/m)
423 2 (2) -P 4ac 2ac
424 139 1 -I 4 2 (D_{4h}^{17}) (I 4/m m m) (I 4/m 2/m 2/m)
425 140 1 -I 4 2c (D_{4h}^{18}) (I 4/m c m) (I 4/m 2/c 2/m)
426 141 1 (1) I 4bw 2bw -1bw (D_{4h}^{19}) (I 4_1/ a m d) (I 4_1/a 2/m 2/d)
427 2 (2) -I 4bd 2
428 142 1 (1) I 4bw 2aw -1bw (D_{4h}^{20}) (I 4_1/ a c d) (I 4_1/a 2/c 2/d)
429 2 (2) -I 4bd 2c

Trigonal 三方晶系

Crystal System No.: 5

Serial No. ITA No. Sub No. Axes, Origin Hall symbol Sch. symbol HM symbol (short) HM symbol (full) PG No. PG (HM) PG (Sch.) LC No. LC (HM)
430 143 1 P 3 (C_3^1) (P 3) (P 3) 16 (3) (C_{3}) 6 (bar{3})
431 144 1 P 31 (C_3^2) (P 3_1) (P 3_1)
432 145 1 P 32 (C_3^3) (P 3_2) (P 3_2)
433 146 1 (H) R 3 (C_3^4) (R 3) (R 3)
434 2 (R) P 3*
435 147 1 -P 3 (C_{3i}^1) (P bar{3}) (P bar{3}) 17 (bar{3}) (C_{3i})
436 148 1 (H) -R 3 (C_{3i}^2) (R bar{3}) (R bar{3})
437 2 (R) -P 3*
438 149 1 P 3 2 (D_3^1) (P 3 1 2) (P 3 1 2) 18 (3 2) (D_3) 7 (bar{3}2m)
439 150 1 P 3 2 (D_3^2) (P 3 2 1) (P 3 2 1)
440 151 1 P 31 2c (0 0 1) (D_3^3) (P 3_1 1 2) (P 3_1 1 2)
441 152 1 P 31 2 (D_3^4) (P 3_1 2 1) (P 3_1 2 1)
442 153 1 P 32 2c (0 0 -1) (D_3^5) (P 3_2 1 2) (P 3_2 1 2)
443 154 1 P 32 2 (D_3^6) (P 3_2 2 1) (P 3_2 2 1)
444 155 1 (H) R 3 2 (D_3^7) (R 3 2) (R 3 2)
445 2 (R) P 3* 2
446 156 1 P 3 -2 (C_{3v}^1) (P 3 m 1) (P 3 m 1) 19 (3 m) (C_{3v})
447 157 1 P 3 -2 (C_{3v}^2) (P 3 1 m) (P 3 1 m)
448 158 1 P 3 -2c (C_{3v}^3) (P 3 c 1) (P 3 c 1)
449 159 1 P 3 -2c (C_{3v}^4) (P 3 1 c) (P 3 1 c)
450 160 1 (H) R 3 -2 (C_{3v}^5) (R 3 m) (R 3 m)
451 2 (R) P 3* -2
452 161 1 (H) R 3 -2c (C_{3v}^6) (R 3 c) (R 3 c)
453 2 (R) P 3* -2n
454 162 1 -P 3 2 (D_{3d}^1) (P bar{3} 1 m) (P bar{3} 1 2/m) 20 (bar{3} m) (D_{3d})
455 163 1 -P 3 2c (D_{3d}^2) (P bar{3} 1 c) (P bar{3} 1 2/c)
456 164 1 -P 3 2 (D_{3d}^3) (P bar{3} m 1) (P bar{3} 2/m 1)
457 165 1 -P 3 2c (D_{3d}^4) (P bar{3} c 1) (P bar{3} 2/c 1)
458 166 1 (H) -R 3 2 (D_{3d}^5) (R bar{3} m) (R bar{3} 2/m)
459 2 (R) -P 3* 2
460 167 1 (H) -R 3 2c (D_{3d}^6) (R bar{3} c) (R bar{3} 2/c)
461 2 (R) -P 3* 2n

Hexagonal 六方晶系

Crystal System No.: 6

Serial No. ITA No. Sub No. Axes, Origin Hall symbol Sch. symbol HM symbol (short) HM symbol (full) PG No. PG (HM) PG (Sch.) LC No. LC (HM)
462 168 1 P 6 (C_6^1) (P 6) (P 6) 21 (6) (C_6) 8 (6/m)
463 169 1 P 61 (C_6^2) (P 6_1) (P 6_1)
464 170 1 P 65 (C_6^3) (P 6_5) (P 6_5)
465 171 1 P 62 (C_6^4) (P 6_2) (P 6_2)
466 172 1 P 64 (C_6^5) (P 6_4) (P 6_4)
467 173 1 P 6c (C_6^6) (P 6_3) (P 6_3)
468 174 1 P -6 (C_{3h}^1) (P bar{6}) (P bar{6}) 22 (bar{6}) (C_{3h})
469 175 1 -P 6 (C_{6h}^1) (P 6/m) (P 6/m) 23 (6/m) (C_{6h})
470 176 1 -P 6c (C_{6h}^2) (P 6_3/m) (P 6_3/m)
471 177 1 P 6 2 (D_6^1) (P 6 2 2) (P 6 2 2) 24 (6 2 2) (D_6) 9 (6/mmm)
472 178 1 P 61 2 (0 0 -1) (D_6^2) (P 6_1 2 2) (P 6_1 2 2)
473 179 1 P 65 2 (0 0 1) (D_6^3) (P 6_5 2 2) (P 6_5 2 2)
474 180 1 P 62 2c (0 0 1) (D_6^4) (P 6_2 2 2) (P 6_2 2 2)
475 181 1 P 64 2c (0 0 -1) (D_6^5) (P 6_4 2 2) (P 6_4 2 2)
476 182 1 P 6c 2c (D_6^6) (P 6_3 2 2) (P 6_3 2 2)
477 183 1 P 6 -2 (C_{6v}^1) (P 6 m m) (P 6 m m) 25 (6 m m) (C_{6v})
478 184 1 P 6 -2c (C_{6v}^2) (P 6 c c) (P 6 c c)
479 185 1 P 6c -2 (C_{6v}^3) (P 6_3 c m) (P 6_3 c m)
480 186 1 P 6c -2c (C_{6v}^4) (P 6_3 m c) (P 6_3 m c)
481 187 1 P -6 2 (D_{3h}^1) (P bar{6} m 2) (P bar{6} m 2) 26 (bar{6} m 2) (D_{3h})
482 188 1 P -6c 2 (D_{3h}^2) (P bar{6} c 2) (P bar{6} c 2)
483 189 1 P -6 -2 (D_{3h}^3) (P bar{6} 2 m) (P bar{6} 2 m)
484 190 1 P -6c -2c (D_{3h}^4) (P bar{6} 2 c) (P bar{6} 2 c)
485 191 1 -P 6 2 (D_{6h}^1) (P 6/m m m) (P 6/m 2/m 2/m) 27 (6/m m m) (D_{6h})
486 192 1 -P 6 2c (D_{6h}^2) (P 6/m c c) (P 6/m 2/c 2/c)
487 193 1 -P 6c 2 (D_{6h}^3) (P 6_3/m c m) (P 6_3/m 2/c 2/m)
488 194 1 -P 6c 2c (D_{6h}^4) (P 6_3/m m c) (P 6_3/m 2/m 2/c)

Cubic 立方晶系

Crystal System No.: 7

Serial No. ITA No. Sub No. Axes, Origin Hall symbol Sch. symbol HM symbol (short) HM symbol (full) PG No. PG (HM) PG (Sch.) LC No. LC (HM)
489 195 1 P 2 2 3 (T^1) (P 2 3) (P 2 3) 28 (2 3) (T) 10 (mbar{3})
490 196 1 F 2 2 3 (T^2) (F 2 3) (F 2 3)
491 197 1 I 2 2 3 (T^3) (I 2 3) (I 2 3)
492 198 1 P 2ac 2ab 3 (T^4) (P 2_1 3) (P 2_1 3)
493 199 1 I 2b 2c 3 (T^5) (I 2_1 3) (I 2_1 3)
494 200 1 -P 2 2 3 (T_h^1) (P m bar{3}) (P 2/m bar{3}) 29 (m bar{3}) (T_h)
495 201 1 (1) P 2 2 3 -1n (T_h^2) (P n bar{3}) (P 2/n bar{3})
496 2 (2) -P 2ab 2bc 3
497 202 1 -F 2 2 3 (T_h^3) (F m bar{3}) (F 2/m bar{3})
498 203 1 (1) F 2 2 3 -1d (T_h^4) (F d bar{3}) (F 2/d bar{3})
499 2 (2) -F 2uv 2vw 3
500 204 1 -I 2 2 3 (T_h^5) (I m bar{3}) (I 2/m bar{3})
501 205 1 -P 2ac 2ab 3 (T_h^6) (P a bar{3}) (P 2_1/a bar{3})
502 206 1 -I 2b 2c 3 (T_h^7) (I a bar{3}) (I 2_1/a bar{3})
503 207 1 P 4 2 3 (O^1) (P 4 3 2) (P 4 3 2) 30 (4 3 2) (O) 11 (mbar{3}m)
504 208 1 P 4n 2 3 (O^2) (P 4_2 3 2) (P 4_2 3 2)
505 209 1 F 4 2 3 (O^3) (F 4 3 2) (F 4 3 2)
506 210 1 F 4d 2 3 (O^4) (F 4_1 3 2) (F 4_1 3 2)
507 211 1 I 4 2 3 (O^5) (I 4 3 2) (I 4 3 2)
508 212 1 P 4acd 2ab 3 (O^6) (P 4_3 3 2) (P 4_3 3 2)
509 213 1 P 4bd 2ab 3 (O^7) (P 4_1 3 2) (P 4_1 3 2)
510 214 1 I 4bd 2c 3 (O^8) (I 4_1 3 2) (I 4_1 3 2)
511 215 1 P -4 2 3 (T_d^1) (P bar{4} 3 m) (P bar{4} 3 m) 31 (bar{4} 3 m) (T_d)
512 216 1 F -4 2 3 (T_d^2) (F bar{4} 3 m) (F bar{4} 3 m)
513 217 1 I -4 2 3 (T_d^3) (I bar{4} 3 m) (I bar{4} 3 m)
514 218 1 P -4n 2 3 (T_d^4) (P bar{4} 3 n) (P bar{4} 3 n)
515 219 1 F -4c 2 3 (T_d^5) (F bar{4} 3 c) (F bar{4} 3 c)
516 220 1 I -4bd 2c 3 (T_d^6) (I bar{4} 3 d) (I bar{4} 3 d)
517 221 1 -P 4 2 3 (O_h^1) (P m bar{3} m) (P 4/m bar{3} 2/m) 32 (m bar{3} m) (O_h)
518 222 1 (1) P 4 2 3 -1n (O_h^2) (P n bar{3} n) (P 4/n bar{3} 2/n)
519 2 (2) -P 4a 2bc 3
520 223 1 -P 4n 2 3 (O_h^3) (P m bar{3} n) (P 4_2/m bar{3} 2/n)
521 224 1 (1) P 4n 2 3 -1n (O_h^4) (P n bar{3} m) (P 4_2/n bar{3} 2/m)
522 2 (2) -P 4bc 2bc 3
523 225 1 -F 4 2 3 (O_h^5) (F m bar{3} m) (F 4/m bar{3} 2/m)
524 226 1 -F 4c 2 3 (O_h^6) (F m bar{3} c) (F 4/m bar{3} 2/c)
525 227 1 (1) F 4d 2 3 -1d (O_h^7) (F d bar{3} m) (F 4_1/d bar{3} 2/m)
526 2 (2) -F 4vw 2vw 3
527 228 1 (1) F 4d 2 3 -1cd (O_h^8) (F d bar{3} c) (F 4_1/d bar{3} 2/c)
528 2 (2) -F 4cvw 2vw 3
529 229 1 -I 4 2 3 (O_h^9) (I m bar{3} m) (I 4/m bar{3} 2/m)
530 230 1 -I 4bd 2c 3 (O_h^{10}) (I a bar{3} d) (I 4_1/a bar{3} 2/d)
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