Polytope of Type {12,2,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,24}*1152
if this polytope has a name.
Group : SmallGroup(1152,119787)
Rank : 4
Schlafli Type : {12,2,24}
Number of vertices, edges, etc : 12, 12, 24, 24
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, {6,2,24}*576
   3-fold quotients : {4,2,24}*384, {12,2,8}*384
   4-fold quotients : {3,2,24}*288, {6,2,12}*288, {12,2,6}*288
   6-fold quotients : {4,2,12}*192, {12,2,4}*192, {2,2,24}*192, {6,2,8}*192
   8-fold quotients : {3,2,12}*144, {12,2,3}*144, {6,2,6}*144
   9-fold quotients : {4,2,8}*128
   12-fold quotients : {3,2,8}*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, {2,2,8}*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)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
s2 := (14,15)(16,17)(18,21)(19,23)(20,22)(24,27)(25,29)(26,28)(31,34)(32,33)
(35,36);;
s3 := (13,19)(14,16)(15,25)(17,20)(18,22)(21,31)(23,26)(24,28)(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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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