Polytope of Type {2,2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,157863)
Rank : 5
Schlafli Type : {2,2,6,12}
Number of vertices, edges, etc : 2, 2, 12, 72, 24
Order of s₀s₁s₂s₃s₄ : 6
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 : {2,2,6,12}*576d
   3-fold quotients : {2,2,6,4}*384
   4-fold quotients : {2,2,6,6}*288a
   6-fold quotients : {2,2,3,4}*192, {2,2,6,4}*192b, {2,2,6,4}*192c
   12-fold quotients : {2,2,3,4}*96, {2,2,2,6}*96, {2,2,6,2}*96
   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 := (3,4);;
s2 := ( 6, 7)(10,11)(14,15)(17,29)(18,31)(19,30)(20,32)(21,33)(22,35)(23,34)
(24,36)(25,37)(26,39)(27,38)(28,40)(42,43)(46,47)(50,51)(53,65)(54,67)(55,66)
(56,68)(57,69)(58,71)(59,70)(60,72)(61,73)(62,75)(63,74)(64,76);;
s3 := ( 5,17)( 6,18)( 7,20)( 8,19)( 9,25)(10,26)(11,28)(12,27)(13,21)(14,22)
(15,24)(16,23)(31,32)(33,37)(34,38)(35,40)(36,39)(41,53)(42,54)(43,56)(44,55)
(45,61)(46,62)(47,64)(48,63)(49,57)(50,58)(51,60)(52,59)(67,68)(69,73)(70,74)
(71,76)(72,75);;
s4 := ( 5,48)( 6,47)( 7,46)( 8,45)( 9,44)(10,43)(11,42)(12,41)(13,52)(14,51)
(15,50)(16,49)(17,60)(18,59)(19,58)(20,57)(21,56)(22,55)(23,54)(24,53)(25,64)
(26,63)(27,62)(28,61)(29,72)(30,71)(31,70)(32,69)(33,68)(34,67)(35,66)(36,65)
(37,76)(38,75)(39,74)(40,73);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := Sym(76)!( 6, 7)(10,11)(14,15)(17,29)(18,31)(19,30)(20,32)(21,33)(22,35)
(23,34)(24,36)(25,37)(26,39)(27,38)(28,40)(42,43)(46,47)(50,51)(53,65)(54,67)
(55,66)(56,68)(57,69)(58,71)(59,70)(60,72)(61,73)(62,75)(63,74)(64,76);
s3 := Sym(76)!( 5,17)( 6,18)( 7,20)( 8,19)( 9,25)(10,26)(11,28)(12,27)(13,21)
(14,22)(15,24)(16,23)(31,32)(33,37)(34,38)(35,40)(36,39)(41,53)(42,54)(43,56)
(44,55)(45,61)(46,62)(47,64)(48,63)(49,57)(50,58)(51,60)(52,59)(67,68)(69,73)
(70,74)(71,76)(72,75);
s4 := Sym(76)!( 5,48)( 6,47)( 7,46)( 8,45)( 9,44)(10,43)(11,42)(12,41)(13,52)
(14,51)(15,50)(16,49)(17,60)(18,59)(19,58)(20,57)(21,56)(22,55)(23,54)(24,53)
(25,64)(26,63)(27,62)(28,61)(29,72)(30,71)(31,70)(32,69)(33,68)(34,67)(35,66)
(36,65)(37,76)(38,75)(39,74)(40,73);
poly := sub<Sym(76)|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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3 >;

to this polytope