Polytope of Type {2,8,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,6,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,152548)
Rank : 5
Schlafli Type : {2,8,6,6}
Number of vertices, edges, etc : 2, 8, 24, 18, 6
Order of s₀s₁s₂s₃s₄ : 24
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 : {2,4,6,6}*576b
   3-fold quotients : {2,8,6,2}*384
   4-fold quotients : {2,2,6,6}*288c
   6-fold quotients : {2,4,6,2}*192a
   8-fold quotients : {2,2,3,6}*144
   9-fold quotients : {2,8,2,2}*128
   12-fold quotients : {2,2,6,2}*96
   18-fold quotients : {2,4,2,2}*64
   24-fold quotients : {2,2,3,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(39,57)
(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)
(51,69)(52,70)(53,71)(54,72)(55,73)(56,74);;
s2 := ( 3,39)( 4,41)( 5,40)( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)(12,48)
(13,50)(14,49)(15,54)(16,56)(17,55)(18,51)(19,53)(20,52)(21,66)(22,68)(23,67)
(24,72)(25,74)(26,73)(27,69)(28,71)(29,70)(30,57)(31,59)(32,58)(33,63)(34,65)
(35,64)(36,60)(37,62)(38,61);;
s3 := ( 3, 7)( 4, 6)( 5, 8)( 9,10)(12,16)(13,15)(14,17)(18,19)(21,25)(22,24)
(23,26)(27,28)(30,34)(31,33)(32,35)(36,37)(39,43)(40,42)(41,44)(45,46)(48,52)
(49,51)(50,53)(54,55)(57,61)(58,60)(59,62)(63,64)(66,70)(67,69)(68,71)
(72,73);;
s4 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)
(67,68)(70,71)(73,74);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(74)!(1,2);
s1 := Sym(74)!(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)
(39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)
(50,68)(51,69)(52,70)(53,71)(54,72)(55,73)(56,74);
s2 := Sym(74)!( 3,39)( 4,41)( 5,40)( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)
(12,48)(13,50)(14,49)(15,54)(16,56)(17,55)(18,51)(19,53)(20,52)(21,66)(22,68)
(23,67)(24,72)(25,74)(26,73)(27,69)(28,71)(29,70)(30,57)(31,59)(32,58)(33,63)
(34,65)(35,64)(36,60)(37,62)(38,61);
s3 := Sym(74)!( 3, 7)( 4, 6)( 5, 8)( 9,10)(12,16)(13,15)(14,17)(18,19)(21,25)
(22,24)(23,26)(27,28)(30,34)(31,33)(32,35)(36,37)(39,43)(40,42)(41,44)(45,46)
(48,52)(49,51)(50,53)(54,55)(57,61)(58,60)(59,62)(63,64)(66,70)(67,69)(68,71)
(72,73);
s4 := Sym(74)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)
(64,65)(67,68)(70,71)(73,74);
poly := sub<Sym(74)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope