Overview
- Group
- SmallGroup(960,8150)
- Rank
- 4
- Schläfli Type
- {10,2,24}
- Vertices, edges, …
- 10, 10, 24, 24
- Order of s0s1s2s3
- 120
- 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
3-fold
4-fold
5-fold
6-fold
8-fold
10-fold
12-fold
15-fold
16-fold
20-fold
24-fold
30-fold
40-fold
60-fold
Covers minimal covers in bold
2-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 := (12,13)(14,15)(16,19)(17,21)(18,20)(22,25)(23,27)(24,26)(29,32)(30,31)(33,34);; s3 := (11,17)(12,14)(13,23)(15,18)(16,20)(19,29)(21,24)(22,26)(25,33)(27,30)(28,31)(32,34);; 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*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(34)!( 3, 4)( 5, 6)( 7, 8)( 9,10); s1 := Sym(34)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10); s2 := Sym(34)!(12,13)(14,15)(16,19)(17,21)(18,20)(22,25)(23,27)(24,26)(29,32)(30,31)(33,34); s3 := Sym(34)!(11,17)(12,14)(13,23)(15,18)(16,20)(19,29)(21,24)(22,26)(25,33)(27,30)(28,31)(32,34); poly := sub<Sym(34)|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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;