Overview
- Group
- SmallGroup(1728,47409)
- Rank
- 6
- Schläfli Type
- {2,6,12,2,3}
- Vertices, edges, …
- 2, 6, 36, 12, 3, 3
- Order of s0s1s2s3s4s5
- 12
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
9-fold
12-fold
18-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3,39)( 4,41)( 5,40)( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)(12,48)(13,50)(14,49)(15,54)(16,56)(17,55)(18,51)(19,53)(20,52)(21,57)(22,59)(23,58)(24,63)(25,65)(26,64)(27,60)(28,62)(29,61)(30,66)(31,68)(32,67)(33,72)(34,74)(35,73)(36,69)(37,71)(38,70);; s2 := ( 3,61)( 4,60)( 5,62)( 6,58)( 7,57)( 8,59)( 9,64)(10,63)(11,65)(12,70)(13,69)(14,71)(15,67)(16,66)(17,68)(18,73)(19,72)(20,74)(21,43)(22,42)(23,44)(24,40)(25,39)(26,41)(27,46)(28,45)(29,47)(30,52)(31,51)(32,53)(33,49)(34,48)(35,50)(36,55)(37,54)(38,56);; s3 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(21,30)(22,32)(23,31)(24,33)(25,35)(26,34)(27,36)(28,38)(29,37)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72)(64,74)(65,73);; s4 := (76,77);; 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, s3*s4*s3*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5*s4*s5, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(77)!(1,2); s1 := Sym(77)!( 3,39)( 4,41)( 5,40)( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)(12,48)(13,50)(14,49)(15,54)(16,56)(17,55)(18,51)(19,53)(20,52)(21,57)(22,59)(23,58)(24,63)(25,65)(26,64)(27,60)(28,62)(29,61)(30,66)(31,68)(32,67)(33,72)(34,74)(35,73)(36,69)(37,71)(38,70); s2 := Sym(77)!( 3,61)( 4,60)( 5,62)( 6,58)( 7,57)( 8,59)( 9,64)(10,63)(11,65)(12,70)(13,69)(14,71)(15,67)(16,66)(17,68)(18,73)(19,72)(20,74)(21,43)(22,42)(23,44)(24,40)(25,39)(26,41)(27,46)(28,45)(29,47)(30,52)(31,51)(32,53)(33,49)(34,48)(35,50)(36,55)(37,54)(38,56); s3 := Sym(77)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(21,30)(22,32)(23,31)(24,33)(25,35)(26,34)(27,36)(28,38)(29,37)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72)(64,74)(65,73); s4 := Sym(77)!(76,77); s5 := Sym(77)!(75,76); poly := sub<Sym(77)|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, s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;