Polytope of Type {2,6,6,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,4,2}*1152f
if this polytope has a name.
Group : SmallGroup(1152,157863)
Rank : 6
Schlafli Type : {2,6,6,4,2}
Number of vertices, edges, etc : 2, 6, 18, 12, 4, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {2,6,3,4,2}*576
3-fold quotients : {2,2,6,4,2}*384b
6-fold quotients : {2,2,3,4,2}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)(32,36)
(33,37)(34,38)(43,47)(44,48)(45,49)(46,50)(55,59)(56,60)(57,61)(58,62)(67,71)
(68,72)(69,73)(70,74);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,31)(16,33)(17,32)(18,34)(19,27)
(20,29)(21,28)(22,30)(23,35)(24,37)(25,36)(26,38)(39,43)(40,45)(41,44)(42,46)
(48,49)(51,67)(52,69)(53,68)(54,70)(55,63)(56,65)(57,64)(58,66)(59,71)(60,73)
(61,72)(62,74);;
s3 := ( 3,51)( 4,52)( 5,54)( 6,53)( 7,59)( 8,60)( 9,62)(10,61)(11,55)(12,56)
(13,58)(14,57)(15,39)(16,40)(17,42)(18,41)(19,47)(20,48)(21,50)(22,49)(23,43)
(24,44)(25,46)(26,45)(27,63)(28,64)(29,66)(30,65)(31,71)(32,72)(33,74)(34,73)
(35,67)(36,68)(37,70)(38,69);;
s4 := ( 3,42)( 4,41)( 5,40)( 6,39)( 7,46)( 8,45)( 9,44)(10,43)(11,50)(12,49)
(13,48)(14,47)(15,54)(16,53)(17,52)(18,51)(19,58)(20,57)(21,56)(22,55)(23,62)
(24,61)(25,60)(26,59)(27,66)(28,65)(29,64)(30,63)(31,70)(32,69)(33,68)(34,67)
(35,74)(36,73)(37,72)(38,71);;
s5 := (75,76);;
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, 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,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s2*s3*s4*s2*s3*s4,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(76)!(1,2);
s1 := Sym(76)!( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)
(32,36)(33,37)(34,38)(43,47)(44,48)(45,49)(46,50)(55,59)(56,60)(57,61)(58,62)
(67,71)(68,72)(69,73)(70,74);
s2 := Sym(76)!( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,31)(16,33)(17,32)(18,34)
(19,27)(20,29)(21,28)(22,30)(23,35)(24,37)(25,36)(26,38)(39,43)(40,45)(41,44)
(42,46)(48,49)(51,67)(52,69)(53,68)(54,70)(55,63)(56,65)(57,64)(58,66)(59,71)
(60,73)(61,72)(62,74);
s3 := Sym(76)!( 3,51)( 4,52)( 5,54)( 6,53)( 7,59)( 8,60)( 9,62)(10,61)(11,55)
(12,56)(13,58)(14,57)(15,39)(16,40)(17,42)(18,41)(19,47)(20,48)(21,50)(22,49)
(23,43)(24,44)(25,46)(26,45)(27,63)(28,64)(29,66)(30,65)(31,71)(32,72)(33,74)
(34,73)(35,67)(36,68)(37,70)(38,69);
s4 := Sym(76)!( 3,42)( 4,41)( 5,40)( 6,39)( 7,46)( 8,45)( 9,44)(10,43)(11,50)
(12,49)(13,48)(14,47)(15,54)(16,53)(17,52)(18,51)(19,58)(20,57)(21,56)(22,55)
(23,62)(24,61)(25,60)(26,59)(27,66)(28,65)(29,64)(30,63)(31,70)(32,69)(33,68)
(34,67)(35,74)(36,73)(37,72)(38,71);
s5 := Sym(76)!(75,76);
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,
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, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s2*s3*s4*s2*s3*s4, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >;
to this polytope