Polytope of Type {4,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,99277)
Rank : 4
Schlafli Type : {4,12,2}
Number of vertices, edges, etc : 24, 144, 72, 2
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 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 : {4,12,2}*576
   4-fold quotients : {4,6,2}*288
   8-fold quotients : {4,6,2}*144
   9-fold quotients : {4,4,2}*128
   18-fold quotients : {4,4,2}*64
   36-fold quotients : {2,4,2}*32, {4,2,2}*32
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope