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}*1152a
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}*576a
   3-fold quotients : {2,8,2,6}*384, {2,8,6,2}*384
   4-fold quotients : {2,2,6,6}*288a
   6-fold quotients : {2,8,2,3}*192, {2,4,2,6}*192, {2,4,6,2}*192a
   9-fold quotients : {2,8,2,2}*128
   12-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96, {2,2,6,2}*96
   18-fold quotients : {2,4,2,2}*64
   24-fold quotients : {2,2,2,3}*48, {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)( 6,42)( 7,44)( 8,43)( 9,45)(10,47)(11,46)(12,48)
(13,50)(14,49)(15,51)(16,53)(17,52)(18,54)(19,56)(20,55)(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);;
s3 := ( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,22)(24,28)
(25,27)(26,29)(30,31)(33,37)(34,36)(35,38)(39,40)(42,46)(43,45)(44,47)(48,49)
(51,55)(52,54)(53,56)(57,58)(60,64)(61,63)(62,65)(66,67)(69,73)(70,72)
(71,74);;
s4 := ( 3, 6)( 4, 7)( 5, 8)(12,15)(13,16)(14,17)(21,24)(22,25)(23,26)(30,33)
(31,34)(32,35)(39,42)(40,43)(41,44)(48,51)(49,52)(50,53)(57,60)(58,61)(59,62)
(66,69)(67,70)(68,71);;
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, s2*s3*s4*s3*s2*s3*s4*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, 
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)( 6,42)( 7,44)( 8,43)( 9,45)(10,47)(11,46)
(12,48)(13,50)(14,49)(15,51)(16,53)(17,52)(18,54)(19,56)(20,55)(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);
s3 := Sym(74)!( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,22)
(24,28)(25,27)(26,29)(30,31)(33,37)(34,36)(35,38)(39,40)(42,46)(43,45)(44,47)
(48,49)(51,55)(52,54)(53,56)(57,58)(60,64)(61,63)(62,65)(66,67)(69,73)(70,72)
(71,74);
s4 := Sym(74)!( 3, 6)( 4, 7)( 5, 8)(12,15)(13,16)(14,17)(21,24)(22,25)(23,26)
(30,33)(31,34)(32,35)(39,42)(40,43)(41,44)(48,51)(49,52)(50,53)(57,60)(58,61)
(59,62)(66,69)(67,70)(68,71);
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, 
s2*s3*s4*s3*s2*s3*s4*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope