Polytope of Type {2,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98807)
Rank : 4
Schlafli Type : {2,8,4}
Number of vertices, edges, etc : 2, 72, 144, 36
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 : {2,8,4}*128b
   18-fold quotients : {2,4,4}*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 := ( 3,48)( 4,50)( 5,49)( 6,51)( 7,53)( 8,52)( 9,54)(10,56)(11,55)(12,39)
(13,41)(14,40)(15,42)(16,44)(17,43)(18,45)(19,47)(20,46)(21,66)(22,68)(23,67)
(24,69)(25,71)(26,70)(27,72)(28,74)(29,73)(30,57)(31,59)(32,58)(33,60)(34,62)
(35,61)(36,63)(37,65)(38,64);;
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, 6)( 4, 7)( 5, 8)(12,15)(13,16)(14,17)(21,33)(22,34)(23,35)(24,30)
(25,31)(26,32)(27,36)(28,37)(29,38)(39,42)(40,43)(41,44)(48,51)(49,52)(50,53)
(57,69)(58,70)(59,71)(60,66)(61,67)(62,68)(63,72)(64,73)(65,74);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1*s2*s3*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope