Polytope of Type {2,2,3,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,3,4}*96
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 5
Schlafli Type : {2,2,3,4}
Number of vertices, edges, etc : 2, 2, 3, 6, 4
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,3,4,2} of size 192
{2,2,3,4,4} of size 768
Vertex Figure Of :
{2,2,2,3,4} of size 192
{3,2,2,3,4} of size 288
{4,2,2,3,4} of size 384
{5,2,2,3,4} of size 480
{6,2,2,3,4} of size 576
{7,2,2,3,4} of size 672
{8,2,2,3,4} of size 768
{9,2,2,3,4} of size 864
{10,2,2,3,4} of size 960
{11,2,2,3,4} of size 1056
{12,2,2,3,4} of size 1152
{13,2,2,3,4} of size 1248
{14,2,2,3,4} of size 1344
{15,2,2,3,4} of size 1440
{17,2,2,3,4} of size 1632
{18,2,2,3,4} of size 1728
{19,2,2,3,4} of size 1824
{20,2,2,3,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,2,3,4}*192, {2,2,3,4}*192, {2,2,6,4}*192b, {2,2,6,4}*192c
3-fold covers : {2,2,9,4}*288, {2,6,3,4}*288, {6,2,3,4}*288
4-fold covers : {8,2,3,4}*384, {2,2,12,4}*384b, {2,2,12,4}*384c, {2,4,6,4}*384b, {4,2,3,4}*384, {4,2,6,4}*384b, {4,2,6,4}*384c, {2,2,3,8}*384, {2,2,6,4}*384, {2,4,3,4}*384b
5-fold covers : {10,2,3,4}*480, {2,2,15,4}*480
6-fold covers : {4,2,9,4}*576, {2,2,9,4}*576, {2,2,18,4}*576b, {2,2,18,4}*576c, {12,2,3,4}*576, {4,6,3,4}*576, {2,2,3,12}*576, {2,2,6,12}*576d, {2,6,3,4}*576, {2,6,6,4}*576d, {2,6,6,4}*576e, {2,6,6,4}*576f, {6,2,3,4}*576, {6,2,6,4}*576b, {6,2,6,4}*576c
7-fold covers : {14,2,3,4}*672, {2,2,21,4}*672
8-fold covers : {16,2,3,4}*768, {2,4,12,4}*768b, {2,4,12,4}*768c, {4,4,6,4}*768b, {4,2,12,4}*768b, {4,2,12,4}*768c, {2,2,3,8}*768, {2,2,6,8}*768a, {2,2,6,4}*768a, {2,2,24,4}*768c, {2,2,24,4}*768d, {2,8,6,4}*768b, {8,2,3,4}*768, {8,2,6,4}*768b, {8,2,6,4}*768c, {4,2,3,8}*768, {2,2,12,4}*768b, {2,2,6,4}*768b, {2,2,12,4}*768c, {2,4,6,4}*768a, {4,2,6,4}*768, {2,2,6,8}*768b, {2,2,6,8}*768c, {4,4,3,4}*768b, {2,8,3,4}*768, {2,4,3,4}*768, {2,4,6,4}*768d, {2,4,6,4}*768e
9-fold covers : {2,2,27,4}*864, {18,2,3,4}*864, {2,6,9,4}*864, {6,2,9,4}*864, {2,6,3,4}*864, {6,6,3,4}*864a, {6,6,3,4}*864b
10-fold covers : {20,2,3,4}*960, {4,2,15,4}*960, {2,2,6,20}*960b, {2,10,6,4}*960b, {10,2,3,4}*960, {10,2,6,4}*960b, {10,2,6,4}*960c, {2,2,15,4}*960, {2,2,30,4}*960b, {2,2,30,4}*960c
11-fold covers : {22,2,3,4}*1056, {2,2,33,4}*1056
12-fold covers : {8,2,9,4}*1152, {2,2,36,4}*1152b, {2,2,36,4}*1152c, {2,4,18,4}*1152b, {4,2,9,4}*1152, {4,2,18,4}*1152b, {4,2,18,4}*1152c, {2,2,9,8}*1152, {24,2,3,4}*1152, {8,6,3,4}*1152, {2,2,18,4}*1152, {2,4,9,4}*1152b, {2,6,12,4}*1152d, {2,6,12,4}*1152e, {2,6,12,4}*1152f, {2,6,12,4}*1152g, {6,2,12,4}*1152b, {6,2,12,4}*1152c, {2,12,6,4}*1152d, {12,2,3,4}*1152, {12,2,6,4}*1152b, {12,2,6,4}*1152c, {4,6,6,4}*1152d, {6,4,6,4}*1152b, {4,2,3,12}*1152, {4,2,6,12}*1152d, {2,2,3,24}*1152, {2,6,3,8}*1152, {6,2,3,8}*1152, {4,6,3,4}*1152, {4,6,6,4}*1152g, {4,6,6,4}*1152h, {2,12,6,4}*1152e, {2,6,3,4}*1152, {2,2,6,12}*1152a, {2,2,6,12}*1152b, {2,6,6,4}*1152a, {2,6,6,4}*1152b, {6,2,6,4}*1152, {2,12,3,4}*1152, {6,4,3,4}*1152
13-fold covers : {26,2,3,4}*1248, {2,2,39,4}*1248
14-fold covers : {28,2,3,4}*1344, {4,2,21,4}*1344, {2,2,6,28}*1344b, {2,14,6,4}*1344b, {14,2,3,4}*1344, {14,2,6,4}*1344b, {14,2,6,4}*1344c, {2,2,21,4}*1344, {2,2,42,4}*1344b, {2,2,42,4}*1344c
15-fold covers : {10,2,9,4}*1440, {2,2,45,4}*1440, {10,6,3,4}*1440, {2,6,15,4}*1440, {6,2,15,4}*1440, {30,2,3,4}*1440
17-fold covers : {34,2,3,4}*1632, {2,2,51,4}*1632
18-fold covers : {4,2,27,4}*1728, {2,2,27,4}*1728, {2,2,54,4}*1728b, {2,2,54,4}*1728c, {36,2,3,4}*1728, {12,2,9,4}*1728, {12,6,3,4}*1728a, {4,6,9,4}*1728, {4,6,3,4}*1728a, {2,2,6,36}*1728c, {2,18,6,4}*1728c, {18,2,3,4}*1728, {18,2,6,4}*1728b, {18,2,6,4}*1728c, {2,2,9,12}*1728, {2,2,18,12}*1728c, {2,6,9,4}*1728, {2,6,18,4}*1728c, {2,6,18,4}*1728d, {2,6,18,4}*1728e, {6,2,9,4}*1728, {6,2,18,4}*1728b, {6,2,18,4}*1728c, {2,2,3,12}*1728, {6,6,3,4}*1728a, {2,2,6,12}*1728d, {6,6,6,4}*1728b, {6,6,6,4}*1728c, {2,6,3,4}*1728, {2,6,6,4}*1728e, {2,6,6,4}*1728f, {2,6,6,4}*1728g, {12,6,3,4}*1728b, {4,6,3,4}*1728b, {6,6,3,4}*1728b, {6,6,6,4}*1728j, {6,6,6,4}*1728k, {6,6,6,4}*1728l, {6,6,6,4}*1728m, {6,6,6,4}*1728n, {2,6,3,12}*1728, {2,6,6,4}*1728i, {2,6,6,12}*1728h, {6,2,3,12}*1728, {6,2,6,12}*1728d
19-fold covers : {38,2,3,4}*1824, {2,2,57,4}*1824
20-fold covers : {40,2,3,4}*1920, {8,2,15,4}*1920, {2,10,12,4}*1920b, {2,10,12,4}*1920c, {10,2,12,4}*1920b, {10,2,12,4}*1920c, {2,20,6,4}*1920b, {20,2,3,4}*1920, {20,2,6,4}*1920b, {20,2,6,4}*1920c, {4,10,6,4}*1920b, {4,2,6,20}*1920b, {10,4,6,4}*1920b, {10,2,3,8}*1920, {2,2,60,4}*1920b, {2,2,60,4}*1920c, {2,4,30,4}*1920b, {4,2,15,4}*1920, {4,2,30,4}*1920b, {4,2,30,4}*1920c, {2,2,15,8}*1920, {2,2,6,20}*1920a, {2,10,6,4}*1920a, {10,2,6,4}*1920, {10,4,3,4}*1920, {2,2,30,4}*1920, {2,4,15,4}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (7,8);;
s3 := (6,7);;
s4 := (5,6)(7,8);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s4*s3*s2*s4*s3*s2*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(8)!(1,2);
s1 := Sym(8)!(3,4);
s2 := Sym(8)!(7,8);
s3 := Sym(8)!(6,7);
s4 := Sym(8)!(5,6)(7,8);
poly := sub<Sym(8)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s4*s3*s2*s4*s3*s2*s4*s3 >;
to this polytope