Polytope of Type {2,12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,12}*576c
if this polytope has a name.
Group : SmallGroup(576,6953)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 12, 72, 12
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,12,2} of size 1152
Vertex Figure Of :
   {2,2,12,12} of size 1152
   {3,2,12,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,6}*288b, {2,6,12}*288c
   3-fold quotients : {2,12,4}*192a
   4-fold quotients : {2,6,6}*144c
   6-fold quotients : {2,12,2}*96, {2,6,4}*96a
   8-fold quotients : {2,3,6}*72
   9-fold quotients : {2,4,4}*64
   12-fold quotients : {2,6,2}*48
   18-fold quotients : {2,2,4}*32, {2,4,2}*32
   24-fold quotients : {2,3,2}*24
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,12}*1152a, {2,24,12}*1152b, {2,12,24}*1152c, {2,24,12}*1152e, {2,12,24}*1152f, {2,12,12}*1152c
   3-fold covers : {2,36,12}*1728b, {2,12,12}*1728a, {6,12,12}*1728e, {6,12,12}*1728f, {2,12,12}*1728h
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope