Polytope of Type {24,2,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,2,12}*1152
if this polytope has a name.
Group : SmallGroup(1152,119787)
Rank : 4
Schlafli Type : {24,2,12}
Number of vertices, edges, etc : 24, 24, 12, 12
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 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 : {12,2,12}*576, {24,2,6}*576
   3-fold quotients : {24,2,4}*384, {8,2,12}*384
   4-fold quotients : {24,2,3}*288, {6,2,12}*288, {12,2,6}*288
   6-fold quotients : {4,2,12}*192, {12,2,4}*192, {24,2,2}*192, {8,2,6}*192
   8-fold quotients : {3,2,12}*144, {12,2,3}*144, {6,2,6}*144
   9-fold quotients : {8,2,4}*128
   12-fold quotients : {8,2,3}*96, {2,2,12}*96, {12,2,2}*96, {4,2,6}*96, {6,2,4}*96
   16-fold quotients : {3,2,6}*72, {6,2,3}*72
   18-fold quotients : {4,2,4}*64, {8,2,2}*64
   24-fold quotients : {3,2,4}*48, {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
   32-fold quotients : {3,2,3}*36
   36-fold quotients : {2,2,4}*32, {4,2,2}*32
   48-fold quotients : {2,2,3}*24, {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(19,22)(20,21)
(23,24);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5, 8)( 6,10)( 9,19)(11,14)(12,16)(15,23)(17,20)
(18,21)(22,24);;
s2 := (26,27)(28,29)(31,34)(32,33)(35,36);;
s3 := (25,31)(26,28)(27,35)(29,32)(30,33)(34,36);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(36)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(19,22)
(20,21)(23,24);
s1 := Sym(36)!( 1, 7)( 2, 4)( 3,13)( 5, 8)( 6,10)( 9,19)(11,14)(12,16)(15,23)
(17,20)(18,21)(22,24);
s2 := Sym(36)!(26,27)(28,29)(31,34)(32,33)(35,36);
s3 := Sym(36)!(25,31)(26,28)(27,35)(29,32)(30,33)(34,36);
poly := sub<Sym(36)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope