Polytope of Type {2,2,6,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,6,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,157863)
Rank : 6
Schlafli Type : {2,2,6,6,3}
Number of vertices, edges, etc : 2, 2, 6, 24, 12, 4
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 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) :
3-fold quotients : {2,2,2,6,3}*384
6-fold quotients : {2,2,2,3,3}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 9,13)(10,14)(11,15)(12,16)(21,25)(22,26)(23,27)(24,28)(33,37)(34,38)
(35,39)(36,40)(45,49)(46,50)(47,51)(48,52)(57,61)(58,62)(59,63)(60,64)(69,73)
(70,74)(71,75)(72,76);;
s3 := ( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,33)(18,35)(19,34)(20,36)(21,29)
(22,31)(23,30)(24,32)(25,37)(26,39)(27,38)(28,40)(41,45)(42,47)(43,46)(44,48)
(50,51)(53,69)(54,71)(55,70)(56,72)(57,65)(58,67)(59,66)(60,68)(61,73)(62,75)
(63,74)(64,76);;
s4 := ( 5,53)( 6,54)( 7,56)( 8,55)( 9,57)(10,58)(11,60)(12,59)(13,61)(14,62)
(15,64)(16,63)(17,41)(18,42)(19,44)(20,43)(21,45)(22,46)(23,48)(24,47)(25,49)
(26,50)(27,52)(28,51)(29,65)(30,66)(31,68)(32,67)(33,69)(34,70)(35,72)(36,71)
(37,73)(38,74)(39,76)(40,75);;
s5 := ( 5,44)( 6,42)( 7,43)( 8,41)( 9,48)(10,46)(11,47)(12,45)(13,52)(14,50)
(15,51)(16,49)(17,68)(18,66)(19,67)(20,65)(21,72)(22,70)(23,71)(24,69)(25,76)
(26,74)(27,75)(28,73)(29,56)(30,54)(31,55)(32,53)(33,60)(34,58)(35,59)(36,57)
(37,64)(38,62)(39,63)(40,61);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s5*s4*s3*s5*s4*s3*s5*s4*s3*s5*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := Sym(76)!( 9,13)(10,14)(11,15)(12,16)(21,25)(22,26)(23,27)(24,28)(33,37)
(34,38)(35,39)(36,40)(45,49)(46,50)(47,51)(48,52)(57,61)(58,62)(59,63)(60,64)
(69,73)(70,74)(71,75)(72,76);
s3 := Sym(76)!( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,33)(18,35)(19,34)(20,36)
(21,29)(22,31)(23,30)(24,32)(25,37)(26,39)(27,38)(28,40)(41,45)(42,47)(43,46)
(44,48)(50,51)(53,69)(54,71)(55,70)(56,72)(57,65)(58,67)(59,66)(60,68)(61,73)
(62,75)(63,74)(64,76);
s4 := Sym(76)!( 5,53)( 6,54)( 7,56)( 8,55)( 9,57)(10,58)(11,60)(12,59)(13,61)
(14,62)(15,64)(16,63)(17,41)(18,42)(19,44)(20,43)(21,45)(22,46)(23,48)(24,47)
(25,49)(26,50)(27,52)(28,51)(29,65)(30,66)(31,68)(32,67)(33,69)(34,70)(35,72)
(36,71)(37,73)(38,74)(39,76)(40,75);
s5 := Sym(76)!( 5,44)( 6,42)( 7,43)( 8,41)( 9,48)(10,46)(11,47)(12,45)(13,52)
(14,50)(15,51)(16,49)(17,68)(18,66)(19,67)(20,65)(21,72)(22,70)(23,71)(24,69)
(25,76)(26,74)(27,75)(28,73)(29,56)(30,54)(31,55)(32,53)(33,60)(34,58)(35,59)
(36,57)(37,64)(38,62)(39,63)(40,61);
poly := sub<Sym(76)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s5*s4*s3*s5*s4*s3*s5*s4*s3*s5*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope