Overview
- Group
- SmallGroup(1600,8167)
- Rank
- 5
- Schläfli Type
- {8,2,5,10}
- Vertices, edges, …
- 8, 8, 5, 25, 10
- 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 := (10,11)(12,13)(14,17)(15,19)(16,18)(20,21)(22,27)(23,26)(24,29)(25,28)(30,33)(31,32);; s3 := ( 9,15)(10,12)(11,22)(13,24)(14,18)(16,20)(17,26)(19,30)(21,25)(23,28)(27,32)(29,31);; s4 := (12,13)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(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,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)!(10,11)(12,13)(14,17)(15,19)(16,18)(20,21)(22,27)(23,26)(24,29)(25,28)(30,33)(31,32); s3 := Sym(33)!( 9,15)(10,12)(11,22)(13,24)(14,18)(16,20)(17,26)(19,30)(21,25)(23,28)(27,32)(29,31); s4 := Sym(33)!(12,13)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(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, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;