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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,8,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,152548)
Rank : 5
Schlafli Type : {2,6,8,6}
Number of vertices, edges, etc : 2, 6, 24, 24, 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 : {2,6,4,6}*576
   3-fold quotients : {2,2,8,6}*384, {2,6,8,2}*384
   4-fold quotients : {2,6,2,6}*288
   6-fold quotients : {2,2,4,6}*192a, {2,6,4,2}*192a
   8-fold quotients : {2,3,2,6}*144, {2,6,2,3}*144
   9-fold quotients : {2,2,8,2}*128
   12-fold quotients : {2,2,2,6}*96, {2,6,2,2}*96
   16-fold quotients : {2,3,2,3}*72
   18-fold quotients : {2,2,4,2}*64
   24-fold quotients : {2,2,2,3}*48, {2,3,2,2}*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 := ( 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);;
s2 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,31)(22,30)(23,32)(24,34)
(25,33)(26,35)(27,37)(28,36)(29,38)(39,58)(40,57)(41,59)(42,61)(43,60)(44,62)
(45,64)(46,63)(47,65)(48,67)(49,66)(50,68)(51,70)(52,69)(53,71)(54,73)(55,72)
(56,74);;
s3 := ( 3,39)( 4,40)( 5,41)( 6,45)( 7,46)( 8,47)( 9,42)(10,43)(11,44)(12,48)
(13,49)(14,50)(15,54)(16,55)(17,56)(18,51)(19,52)(20,53)(21,66)(22,67)(23,68)
(24,72)(25,73)(26,74)(27,69)(28,70)(29,71)(30,57)(31,58)(32,59)(33,63)(34,64)
(35,65)(36,60)(37,61)(38,62);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope