Polytope of Type {4,2,2,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,2,24}*768
if this polytope has a name.
Group : SmallGroup(768,1044763)
Rank : 5
Schlafli Type : {4,2,2,24}
Number of vertices, edges, etc : 4, 4, 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 :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,2,12}*384, {2,2,2,24}*384
   3-fold quotients : {4,2,2,8}*256
   4-fold quotients : {2,2,2,12}*192, {4,2,2,6}*192
   6-fold quotients : {4,2,2,4}*128, {2,2,2,8}*128
   8-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96
   12-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   16-fold quotients : {2,2,2,3}*48
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(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*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, s0*s1*s0*s1*s0*s1*s0*s1, 
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)!(2,3);
s1 := Sym(30)!(1,2)(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*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, 
s0*s1*s0*s1*s0*s1*s0*s1, 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