Overview
- Group
- SmallGroup(1600,8167)
- Rank
- 5
- Schläfli Type
- {8,2,10,5}
- Vertices, edges, …
- 8, 8, 10, 25, 5
- Order of s0s1s2s3s4
- 40
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
5-fold
10-fold
20-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5)(6,7);; s1 := (1,2)(3,4)(5,6)(7,8);; s2 := (12,13)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33);; s3 := ( 9,12)(10,18)(11,15)(13,20)(14,26)(16,28)(17,22)(19,24)(23,32)(25,29)(27,30)(31,33);; s4 := ( 9,10)(11,14)(12,16)(13,15)(18,23)(19,22)(20,25)(21,24)(26,27)(28,31)(29,30)(32,33);; 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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(33)!(2,3)(4,5)(6,7); s1 := Sym(33)!(1,2)(3,4)(5,6)(7,8); s2 := Sym(33)!(12,13)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33); s3 := Sym(33)!( 9,12)(10,18)(11,15)(13,20)(14,26)(16,28)(17,22)(19,24)(23,32)(25,29)(27,30)(31,33); s4 := Sym(33)!( 9,10)(11,14)(12,16)(13,15)(18,23)(19,22)(20,25)(21,24)(26,27)(28,31)(29,30)(32,33); poly := sub<Sym(33)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;