Polytope of Type {2,2,6,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,6,4}*1152e
if this polytope has a name.
Group : SmallGroup(1152,157863)
Rank : 6
Schlafli Type : {2,2,6,6,4}
Number of vertices, edges, etc : 2, 2, 6, 18, 12, 4
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 : {2,2,6,3,4}*576
3-fold quotients : {2,2,2,6,4}*384c
6-fold quotients : {2,2,2,3,4}*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)( 9,61)(10,62)(11,64)(12,63)(13,57)(14,58)
(15,60)(16,59)(17,41)(18,42)(19,44)(20,43)(21,49)(22,50)(23,52)(24,51)(25,45)
(26,46)(27,48)(28,47)(29,65)(30,66)(31,68)(32,67)(33,73)(34,74)(35,76)(36,75)
(37,69)(38,70)(39,72)(40,71);;
s5 := ( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)
(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)
(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)(66,67)
(69,72)(70,71)(73,76)(74,75);;
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*s4*s5, s5*s4*s3*s5*s4*s5*s4*s3*s4,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 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)( 9,61)(10,62)(11,64)(12,63)(13,57)
(14,58)(15,60)(16,59)(17,41)(18,42)(19,44)(20,43)(21,49)(22,50)(23,52)(24,51)
(25,45)(26,46)(27,48)(28,47)(29,65)(30,66)(31,68)(32,67)(33,73)(34,74)(35,76)
(36,75)(37,69)(38,70)(39,72)(40,71);
s5 := Sym(76)!( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)
(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)
(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)
(66,67)(69,72)(70,71)(73,76)(74,75);
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*s4*s5,
s5*s4*s3*s5*s4*s5*s4*s3*s4, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
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