Polytope of Type {2,6,6,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,8}*1152a
if this polytope has a name.
Group : SmallGroup(1152,152548)
Rank : 5
Schlafli Type : {2,6,6,8}
Number of vertices, edges, etc : 2, 6, 18, 24, 8
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 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 : {2,6,6,4}*576a
3-fold quotients : {2,2,6,8}*384, {2,6,2,8}*384
4-fold quotients : {2,6,6,2}*288a
6-fold quotients : {2,3,2,8}*192, {2,2,6,4}*192a, {2,6,2,4}*192
9-fold quotients : {2,2,2,8}*128
12-fold quotients : {2,3,2,4}*96, {2,2,6,2}*96, {2,6,2,2}*96
18-fold quotients : {2,2,2,4}*64
24-fold quotients : {2,2,3,2}*48, {2,3,2,2}*48
36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)
(67,68)(70,71)(73,74);;
s2 := ( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,22)(24,28)
(25,27)(26,29)(30,31)(33,37)(34,36)(35,38)(39,40)(42,46)(43,45)(44,47)(48,49)
(51,55)(52,54)(53,56)(57,58)(60,64)(61,63)(62,65)(66,67)(69,73)(70,72)
(71,74);;
s3 := ( 3, 6)( 4, 7)( 5, 8)(12,15)(13,16)(14,17)(21,33)(22,34)(23,35)(24,30)
(25,31)(26,32)(27,36)(28,37)(29,38)(39,60)(40,61)(41,62)(42,57)(43,58)(44,59)
(45,63)(46,64)(47,65)(48,69)(49,70)(50,71)(51,66)(52,67)(53,68)(54,72)(55,73)
(56,74);;
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);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)
(64,65)(67,68)(70,71)(73,74);
s2 := Sym(74)!( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,22)
(24,28)(25,27)(26,29)(30,31)(33,37)(34,36)(35,38)(39,40)(42,46)(43,45)(44,47)
(48,49)(51,55)(52,54)(53,56)(57,58)(60,64)(61,63)(62,65)(66,67)(69,73)(70,72)
(71,74);
s3 := Sym(74)!( 3, 6)( 4, 7)( 5, 8)(12,15)(13,16)(14,17)(21,33)(22,34)(23,35)
(24,30)(25,31)(26,32)(27,36)(28,37)(29,38)(39,60)(40,61)(41,62)(42,57)(43,58)
(44,59)(45,63)(46,64)(47,65)(48,69)(49,70)(50,71)(51,66)(52,67)(53,68)(54,72)
(55,73)(56,74);
s4 := Sym(74)!( 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);
poly := sub<Sym(74)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, 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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope