Overview
- Group
- SmallGroup(1792,1083553)
- Rank
- 4
- Schläfli Type
- {2,7,4}
- Vertices, edges, …
- 2, 112, 224, 64
- 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 := ( 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);; s2 := ( 4,35)( 5,27)( 6,59)( 7,51)( 8,19)( 9,43)(10,11)(12,42)(13,34)(14,66)(15,58)(16,26)(17,50)(20,40)(21,32)(22,64)(23,56)(25,48)(28,37)(30,61)(31,53)(33,45)(38,60)(39,52)(41,44)(46,65)(47,57)(54,63);; s3 := ( 3,21)( 4,22)( 5,19)( 6,20)( 7,25)( 8,26)( 9,23)(10,24)(11,29)(12,30)(13,27)(14,28)(15,33)(16,34)(17,31)(18,32)(35,53)(36,54)(37,51)(38,52)(39,57)(40,58)(41,55)(42,56)(43,61)(44,62)(45,59)(46,60)(47,65)(48,66)(49,63)(50,64);; 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,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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)!( 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); s2 := Sym(66)!( 4,35)( 5,27)( 6,59)( 7,51)( 8,19)( 9,43)(10,11)(12,42)(13,34)(14,66)(15,58)(16,26)(17,50)(20,40)(21,32)(22,64)(23,56)(25,48)(28,37)(30,61)(31,53)(33,45)(38,60)(39,52)(41,44)(46,65)(47,57)(54,63); s3 := Sym(66)!( 3,21)( 4,22)( 5,19)( 6,20)( 7,25)( 8,26)( 9,23)(10,24)(11,29)(12,30)(13,27)(14,28)(15,33)(16,34)(17,31)(18,32)(35,53)(36,54)(37,51)(38,52)(39,57)(40,58)(41,55)(42,56)(43,61)(44,62)(45,59)(46,60)(47,65)(48,66)(49,63)(50,64); 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, s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 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 >;