Polytope of Type {2,4,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,8}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97552)
Rank : 4
Schlafli Type : {2,4,8}
Number of vertices, edges, etc : 2, 36, 144, 72
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 : {2,4,4}*576
   4-fold quotients : {2,4,4}*288
   8-fold quotients : {2,4,4}*144
   9-fold quotients : {2,4,8}*128a
   18-fold quotients : {2,4,4}*64, {2,2,8}*64
   36-fold quotients : {2,2,4}*32, {2,4,2}*32
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)
(34,37)(35,38)(42,45)(43,46)(44,47)(51,54)(52,55)(53,56)(60,63)(61,64)(62,65)
(69,72)(70,73)(71,74);;
s2 := ( 4, 6)( 5, 9)( 8,10)(13,15)(14,18)(17,19)(21,30)(22,33)(23,36)(24,31)
(25,34)(26,37)(27,32)(28,35)(29,38)(39,57)(40,60)(41,63)(42,58)(43,61)(44,64)
(45,59)(46,62)(47,65)(48,66)(49,69)(50,72)(51,67)(52,70)(53,73)(54,68)(55,71)
(56,74);;
s3 := ( 3,40)( 4,39)( 5,41)( 6,43)( 7,42)( 8,44)( 9,46)(10,45)(11,47)(12,49)
(13,48)(14,50)(15,52)(16,51)(17,53)(18,55)(19,54)(20,56)(21,67)(22,66)(23,68)
(24,70)(25,69)(26,71)(27,73)(28,72)(29,74)(30,58)(31,57)(32,59)(33,61)(34,60)
(35,62)(36,64)(37,63)(38,65);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)
(33,36)(34,37)(35,38)(42,45)(43,46)(44,47)(51,54)(52,55)(53,56)(60,63)(61,64)
(62,65)(69,72)(70,73)(71,74);
s2 := Sym(74)!( 4, 6)( 5, 9)( 8,10)(13,15)(14,18)(17,19)(21,30)(22,33)(23,36)
(24,31)(25,34)(26,37)(27,32)(28,35)(29,38)(39,57)(40,60)(41,63)(42,58)(43,61)
(44,64)(45,59)(46,62)(47,65)(48,66)(49,69)(50,72)(51,67)(52,70)(53,73)(54,68)
(55,71)(56,74);
s3 := Sym(74)!( 3,40)( 4,39)( 5,41)( 6,43)( 7,42)( 8,44)( 9,46)(10,45)(11,47)
(12,49)(13,48)(14,50)(15,52)(16,51)(17,53)(18,55)(19,54)(20,56)(21,67)(22,66)
(23,68)(24,70)(25,69)(26,71)(27,73)(28,72)(29,74)(30,58)(31,57)(32,59)(33,61)
(34,60)(35,62)(36,64)(37,63)(38,65);
poly := sub<Sym(74)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;

to this polytope