Polytope of Type {4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4}*8
Also Known As : square, quadrangle, 2-cube, {4}. if this polytope has another name.
Group : SmallGroup(8,3)
Rank : 2
Schlafli Type : {4}
Number of vertices, edges, etc : 4, 4
Order of s0s1 : 4
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,2} of size 16
{4,3} of size 24
{4,4} of size 32
{4,6} of size 48
{4,3} of size 48
{4,6} of size 48
{4,6} of size 48
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Vertex Figure Of :
{2,4} of size 16
{3,4} of size 24
{4,4} of size 32
{6,4} of size 48
{3,4} of size 48
{6,4} of size 48
{6,4} of size 48
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Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {8}*16
3-fold covers : {12}*24
4-fold covers : {16}*32
5-fold covers : {20}*40
6-fold covers : {24}*48
7-fold covers : {28}*56
8-fold covers : {32}*64
9-fold covers : {36}*72
10-fold covers : {40}*80
11-fold covers : {44}*88
12-fold covers : {48}*96
13-fold covers : {52}*104
14-fold covers : {56}*112
15-fold covers : {60}*120
16-fold covers : {64}*128
17-fold covers : {68}*136
18-fold covers : {72}*144
19-fold covers : {76}*152
20-fold covers : {80}*160
21-fold covers : {84}*168
22-fold covers : {88}*176
23-fold covers : {92}*184
24-fold covers : {96}*192
25-fold covers : {100}*200
26-fold covers : {104}*208
27-fold covers : {108}*216
28-fold covers : {112}*224
29-fold covers : {116}*232
30-fold covers : {120}*240
31-fold covers : {124}*248
32-fold covers : {128}*256
33-fold covers : {132}*264
34-fold covers : {136}*272
35-fold covers : {140}*280
36-fold covers : {144}*288
37-fold covers : {148}*296
38-fold covers : {152}*304
39-fold covers : {156}*312
40-fold covers : {160}*320
41-fold covers : {164}*328
42-fold covers : {168}*336
43-fold covers : {172}*344
44-fold covers : {176}*352
45-fold covers : {180}*360
46-fold covers : {184}*368
47-fold covers : {188}*376
48-fold covers : {192}*384
49-fold covers : {196}*392
50-fold covers : {200}*400
51-fold covers : {204}*408
52-fold covers : {208}*416
53-fold covers : {212}*424
54-fold covers : {216}*432
55-fold covers : {220}*440
56-fold covers : {224}*448
57-fold covers : {228}*456
58-fold covers : {232}*464
59-fold covers : {236}*472
60-fold covers : {240}*480
61-fold covers : {244}*488
62-fold covers : {248}*496
63-fold covers : {252}*504
64-fold covers : {256}*512
65-fold covers : {260}*520
66-fold covers : {264}*528
67-fold covers : {268}*536
68-fold covers : {272}*544
69-fold covers : {276}*552
70-fold covers : {280}*560
71-fold covers : {284}*568
72-fold covers : {288}*576
73-fold covers : {292}*584
74-fold covers : {296}*592
75-fold covers : {300}*600
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247-fold covers : {988}*1976
248-fold covers : {992}*1984
249-fold covers : {996}*1992
250-fold covers : {1000}*2000
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(4)!(2,3);
s1 := Sym(4)!(1,2)(3,4);
poly := sub<Sym(4)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope