Polytope of Type {2,6,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,134264)
Rank : 5
Schlafli Type : {2,6,12,4}
Number of vertices, edges, etc : 2, 6, 36, 24, 4
Order of s₀s₁s₂s₃s₄ : 12
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 : {2,6,12,2}*576b, {2,6,6,4}*576b
   3-fold quotients : {2,2,12,4}*384a
   4-fold quotients : {2,6,6,2}*288b
   6-fold quotients : {2,2,12,2}*192, {2,2,6,4}*192a
   8-fold quotients : {2,6,3,2}*144
   9-fold quotients : {2,2,4,4}*128
   12-fold quotients : {2,2,6,2}*96
   18-fold quotients : {2,2,2,4}*64, {2,2,4,2}*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 := ( 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)( 6,10)( 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)(39,58)(40,57)(41,59)(42,64)(43,63)
(44,65)(45,61)(46,60)(47,62)(48,67)(49,66)(50,68)(51,73)(52,72)(53,74)(54,70)
(55,69)(56,71);;
s3 := ( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,45)(10,47)(11,46)(12,51)
(13,53)(14,52)(15,48)(16,50)(17,49)(18,54)(19,56)(20,55)(21,60)(22,62)(23,61)
(24,57)(25,59)(26,58)(27,63)(28,65)(29,64)(30,69)(31,71)(32,70)(33,66)(34,68)
(35,67)(36,72)(37,74)(38,73);;
s4 := (39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(57,66)
(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74);;
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, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*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)( 6,10)( 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)(39,58)(40,57)(41,59)(42,64)
(43,63)(44,65)(45,61)(46,60)(47,62)(48,67)(49,66)(50,68)(51,73)(52,72)(53,74)
(54,70)(55,69)(56,71);
s3 := Sym(74)!( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,45)(10,47)(11,46)
(12,51)(13,53)(14,52)(15,48)(16,50)(17,49)(18,54)(19,56)(20,55)(21,60)(22,62)
(23,61)(24,57)(25,59)(26,58)(27,63)(28,65)(29,64)(30,69)(31,71)(32,70)(33,66)
(34,68)(35,67)(36,72)(37,74)(38,73);
s4 := Sym(74)!(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)
(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74);
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, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope