Overview
- Group
- SmallGroup(560,176)
- Rank
- 4
- Schläfli Type
- {10,2,14}
- Vertices, edges, …
- 10, 10, 14, 14
- Order of s0s1s2s3
- 70
- Order of s0s1s2s3s2s1
- 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
7-fold
10-fold
14-fold
35-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);; s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);; s2 := (13,14)(15,16)(17,18)(19,20)(21,22)(23,24);; s3 := (11,15)(12,13)(14,19)(16,17)(18,23)(20,21)(22,24);; 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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(24)!( 3, 4)( 5, 6)( 7, 8)( 9,10); s1 := Sym(24)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10); s2 := Sym(24)!(13,14)(15,16)(17,18)(19,20)(21,22)(23,24); s3 := Sym(24)!(11,15)(12,13)(14,19)(16,17)(18,23)(20,21)(22,24); poly := sub<Sym(24)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;