Polytope of Type {2,3,6,8,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6,8,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,152550)
Rank : 6
Schlafli Type : {2,3,6,8,2}
Number of vertices, edges, etc : 2, 3, 9, 24, 8, 2
Order of s0s1s2s3s4s5 : 24
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) :
2-fold quotients : {2,3,6,4,2}*576
3-fold quotients : {2,3,2,8,2}*384
4-fold quotients : {2,3,6,2,2}*288
6-fold quotients : {2,3,2,4,2}*192
12-fold quotients : {2,3,2,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
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)(40,41)(42,45)(43,47)(44,46)(49,50)
(51,54)(52,56)(53,55)(58,59)(60,63)(61,65)(62,64)(67,68)(69,72)(70,74)
(71,73);;
s2 := ( 3, 7)( 4, 6)( 5, 8)( 9,10)(12,16)(13,15)(14,17)(18,19)(21,25)(22,24)
(23,26)(27,28)(30,34)(31,33)(32,35)(36,37)(39,43)(40,42)(41,44)(45,46)(48,52)
(49,51)(50,53)(54,55)(57,61)(58,60)(59,62)(63,64)(66,70)(67,69)(68,71)
(72,73);;
s3 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)(24,36)
(25,37)(26,38)(27,33)(28,34)(29,35)(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);;
s4 := ( 3,39)( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,48)
(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,66)(22,67)(23,68)
(24,69)(25,70)(26,71)(27,72)(28,73)(29,74)(30,57)(31,58)(32,59)(33,60)(34,61)
(35,62)(36,63)(37,64)(38,65);;
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,
s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s3*s4*s3*s4*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)!( 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)(40,41)(42,45)(43,47)(44,46)
(49,50)(51,54)(52,56)(53,55)(58,59)(60,63)(61,65)(62,64)(67,68)(69,72)(70,74)
(71,73);
s2 := Sym(76)!( 3, 7)( 4, 6)( 5, 8)( 9,10)(12,16)(13,15)(14,17)(18,19)(21,25)
(22,24)(23,26)(27,28)(30,34)(31,33)(32,35)(36,37)(39,43)(40,42)(41,44)(45,46)
(48,52)(49,51)(50,53)(54,55)(57,61)(58,60)(59,62)(63,64)(66,70)(67,69)(68,71)
(72,73);
s3 := Sym(76)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)
(24,36)(25,37)(26,38)(27,33)(28,34)(29,35)(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);
s4 := Sym(76)!( 3,39)( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)
(12,48)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,66)(22,67)
(23,68)(24,69)(25,70)(26,71)(27,72)(28,73)(29,74)(30,57)(31,58)(32,59)(33,60)
(34,61)(35,62)(36,63)(37,64)(38,65);
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, s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope