# 立方体堆砌

{4,3}

{4}

W1, G22

(i, j, k)

## 对称性

（字母表示）

Pm3m
{4,3,4} 1: aaaa/aaaa

[4,31,1]
Fm3m
{4,31,1} 2: abba/baab

[4,3,4]
Pm3m
t0,3{4,3,4} 4: abbc/bccd

[4,3,4,2,∞] {4,4}×t{∞} 2: aaaa/bbbb

[4,3,4,2,∞] t1{4,4}×{∞} 2: abba/abba

[∞,2,∞,2,∞] t{∞}×t{∞}×{∞} 4: abcd/abcd

[∞,2,∞,2,∞] t{∞}×t{∞}×t{∞} 8: abcd/efgh

[ ], (*)
Order 2
[ ]+, (1)
[2,2], (*222)
Order 8
[2,2]+, (222)
[4,2], (*422)
Order 16
[4,2]+, (422)
[3], (*33)
Order 6
[3]+, (33)
[4,3], (*432)
Order 48
[4,3]+, (432)

Pm (6)
P1 (1)
Pmmm (47)
P222 (16)
P4/mmm (123)
P422 (89)
R3m (160)
R3 (146)
Pm3m (221)
P432 (207)

- -

## 相關多面體和鑲嵌

{p,3,4}

{4,3,4}

{7,3,4}

{8,3,4}

... {∞,3,4}

{3,3}

{4,3}

{5,3}

{6,3}

{7,3}

{8,3}

{∞,3}

（堆砌）
Pm3m
(221)
4:2 [4,3,4] ×1 1, 2, 3, 4,
5, 6
Fm3m
(225)
2:2 [1+,4,3,4]
↔ [4,31,1]

Half 7, 11, 12, 13
I43m
(217)
4o:2 [[(4,3,4,2+)]] Half × 2 (7),
Fd3m
(227)
2+:2 [[1+,4,3,4,1+]]
↔ [[3[4]]]

Quarter × 2 10,
Im3m
(229)
8o:2 [[4,3,4]] ×2

(1), 8, 9

（堆砌）
Fm3m
(225)
2:2 [4,31,1]
↔ [4,3,4,1+]

×1 1, 2, 3, 4
Fm3m
(225)
2:2 <[1+,4,31,1]>
↔ <[3[4]]>

×2 (1), (3)
Pm3m
(221)
4:2 <[4,31,1]> ×2

5, 6, 7, (6), 9, 10, 11

（堆砌）
F43m
(216)
1o:2 a1 [3[4]] ×1 (None)
Fd3m
(227)
2+:2 p2 [[3[4]]]
×2  3
Fm3m
(225)
2:2 d2 <[3[4]]>
↔ [4,3,31,1]

×2  1, 2
Pm3m
(221)
4:2 d4 [2[3[4]]]
↔ [4,3,4]

×4  4
Im3m
(229)
8o:2 r8 [4[3[4]]]
↔ [[4,3,4]]

×8  5,  (*)

## 参考

1. ^
2. ^ John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (2008) The Symmetries of Things, ISBN 978-1-56881-220-5 (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, Architectonic and Catoptric tessellations, p 292-298, includes all the nonprismatic forms)
3. ^ Richard Klitzing, chon [2014-04-27]
4. ^ [2], A000029 6-1 cases, skipping one with zero marks
• H.S.M.考克斯特 Regular Polytopes, (第三版, 1973), Dover参与编辑, ISBN 0-486-61480-8 p. 296, Table II:正堆砌
• George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) （包含11个凸半正镶嵌、28个凸半正堆砌、和143个凸半正四维砌的全表）
• Branko Grünbaum, 三维正镶嵌. Geombinatorics 4(1994), 49 - 56.
• Kaleidoscopes: Selected Writings of H.S.M. Coxeter, F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication参与编辑, 1995, ISBN 978-0-471-01003-6 [1]
• (22页) H.S.M.考克斯特, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 半正空间镶嵌)
• A. Andreini, Sulle reti di poliedri regolari e semiregolari e sulle corrispondenti reti correlative (On the regular and semiregular nets of polyhedra and on the corresponding correlative nets), Mem. Società Italiana della Scienze, Ser.3, 14 (1905) 75–129.
• Richard Klitzing, 3D Euclidean Honeycombs, x4o3o4o - chon - O1
• Uniform Honeycombs in 3-Space: 01-Chon