Overview
- Group
- SmallGroup(1792,1083553)
- Rank
- 4
- Schläfli Type
- {2,4,7}
- Vertices, edges, …
- 2, 64, 224, 112
- Order of s0s1s2s3
- 14
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3,39)( 4,40)( 5,41)( 6,42)( 7,35)( 8,36)( 9,37)(10,38)(11,47)(12,48)(13,49)(14,50)(15,43)(16,44)(17,45)(18,46)(19,55)(20,56)(21,57)(22,58)(23,51)(24,52)(25,53)(26,54)(27,63)(28,64)(29,65)(30,66)(31,59)(32,60)(33,61)(34,62);; s2 := ( 4,51)( 5,19)( 6,35)( 7,27)( 8,43)( 9,11)(10,59)(12,57)(13,25)(14,41)(15,33)(16,49)(18,65)(20,53)(22,37)(23,29)(24,45)(26,61)(28,55)(30,39)(32,47)(34,63)(36,54)(40,46)(42,62)(44,56)(50,64)(58,60);; s3 := ( 4,59)( 5,51)( 6,11)( 7,35)( 8,27)( 9,19)(10,43)(12,62)(13,54)(15,38)(16,30)(17,22)(18,46)(20,65)(21,57)(23,41)(24,33)(26,49)(28,64)(29,56)(31,40)(34,48)(36,63)(37,55)(42,47)(44,66)(45,58)(52,61);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(66)!(1,2); s1 := Sym(66)!( 3,39)( 4,40)( 5,41)( 6,42)( 7,35)( 8,36)( 9,37)(10,38)(11,47)(12,48)(13,49)(14,50)(15,43)(16,44)(17,45)(18,46)(19,55)(20,56)(21,57)(22,58)(23,51)(24,52)(25,53)(26,54)(27,63)(28,64)(29,65)(30,66)(31,59)(32,60)(33,61)(34,62); s2 := Sym(66)!( 4,51)( 5,19)( 6,35)( 7,27)( 8,43)( 9,11)(10,59)(12,57)(13,25)(14,41)(15,33)(16,49)(18,65)(20,53)(22,37)(23,29)(24,45)(26,61)(28,55)(30,39)(32,47)(34,63)(36,54)(40,46)(42,62)(44,56)(50,64)(58,60); s3 := Sym(66)!( 4,59)( 5,51)( 6,11)( 7,35)( 8,27)( 9,19)(10,43)(12,62)(13,54)(15,38)(16,30)(17,22)(18,46)(20,65)(21,57)(23,41)(24,33)(26,49)(28,64)(29,56)(31,40)(34,48)(36,63)(37,55)(42,47)(44,66)(45,58)(52,61); poly := sub<Sym(66)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3 >;