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Polytope of Type {2,2,2,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,24}*384
if this polytope has a name.
Group : SmallGroup(384,19724)
Rank : 5
Schlafli Type : {2,2,2,24}
Number of vertices, edges, etc : 2, 2, 2, 24, 24
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,2,24,2} of size 768
Vertex Figure Of :
{2,2,2,2,24} of size 768
{3,2,2,2,24} of size 1152
{5,2,2,2,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,12}*192
3-fold quotients : {2,2,2,8}*128
4-fold quotients : {2,2,2,6}*96
6-fold quotients : {2,2,2,4}*64
8-fold quotients : {2,2,2,3}*48
12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,2,4,24}*768a, {2,4,2,24}*768, {4,2,2,24}*768, {2,2,2,48}*768
3-fold covers : {2,2,2,72}*1152, {2,2,6,24}*1152b, {2,2,6,24}*1152c, {2,6,2,24}*1152, {6,2,2,24}*1152
5-fold covers : {2,2,2,120}*1920, {2,2,10,24}*1920, {2,10,2,24}*1920, {10,2,2,24}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,21)(19,23)(20,22)(25,28)(26,27)
(29,30);;
s4 := ( 7,13)( 8,10)( 9,19)(11,14)(12,16)(15,25)(17,20)(18,22)(21,29)(23,26)
(24,27)(28,30);;
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, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(30)!(1,2);
s1 := Sym(30)!(3,4);
s2 := Sym(30)!(5,6);
s3 := Sym(30)!( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,21)(19,23)(20,22)(25,28)
(26,27)(29,30);
s4 := Sym(30)!( 7,13)( 8,10)( 9,19)(11,14)(12,16)(15,25)(17,20)(18,22)(21,29)
(23,26)(24,27)(28,30);
poly := sub<Sym(30)|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,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope