Polytope of Type {4,2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,6,12}*1152c
if this polytope has a name.
Group : SmallGroup(1152,136342)
Rank : 5
Schlafli Type : {4,2,6,12}
Number of vertices, edges, etc : 4, 4, 6, 36, 12
Order of s₀s₁s₂s₃s₄ : 12
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 : {2,2,6,12}*576b, {4,2,6,6}*576b
   3-fold quotients : {4,2,2,12}*384
   4-fold quotients : {4,2,6,3}*288, {2,2,6,6}*288b
   6-fold quotients : {2,2,2,12}*192, {4,2,2,6}*192
   8-fold quotients : {2,2,6,3}*144
   9-fold quotients : {4,2,2,4}*128
   12-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96
   18-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   24-fold quotients : {2,2,2,3}*48
   36-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 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)
(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)(66,67)
(69,70)(72,73)(75,76);;
s3 := ( 5,42)( 6,41)( 7,43)( 8,48)( 9,47)(10,49)(11,45)(12,44)(13,46)(14,51)
(15,50)(16,52)(17,57)(18,56)(19,58)(20,54)(21,53)(22,55)(23,69)(24,68)(25,70)
(26,75)(27,74)(28,76)(29,72)(30,71)(31,73)(32,60)(33,59)(34,61)(35,66)(36,65)
(37,67)(38,63)(39,62)(40,64);;
s4 := ( 5,62)( 6,64)( 7,63)( 8,59)( 9,61)(10,60)(11,65)(12,67)(13,66)(14,71)
(15,73)(16,72)(17,68)(18,70)(19,69)(20,74)(21,76)(22,75)(23,44)(24,46)(25,45)
(26,41)(27,43)(28,42)(29,47)(30,49)(31,48)(32,53)(33,55)(34,54)(35,50)(36,52)
(37,51)(38,56)(39,58)(40,57);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(76)!(2,3);
s1 := Sym(76)!(1,2)(3,4);
s2 := Sym(76)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)
(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)
(66,67)(69,70)(72,73)(75,76);
s3 := Sym(76)!( 5,42)( 6,41)( 7,43)( 8,48)( 9,47)(10,49)(11,45)(12,44)(13,46)
(14,51)(15,50)(16,52)(17,57)(18,56)(19,58)(20,54)(21,53)(22,55)(23,69)(24,68)
(25,70)(26,75)(27,74)(28,76)(29,72)(30,71)(31,73)(32,60)(33,59)(34,61)(35,66)
(36,65)(37,67)(38,63)(39,62)(40,64);
s4 := Sym(76)!( 5,62)( 6,64)( 7,63)( 8,59)( 9,61)(10,60)(11,65)(12,67)(13,66)
(14,71)(15,73)(16,72)(17,68)(18,70)(19,69)(20,74)(21,76)(22,75)(23,44)(24,46)
(25,45)(26,41)(27,43)(28,42)(29,47)(30,49)(31,48)(32,53)(33,55)(34,54)(35,50)
(36,52)(37,51)(38,56)(39,58)(40,57);
poly := sub<Sym(76)|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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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