Overview
- Group
- SmallGroup(1440,3578)
- Rank
- 4
- Schläfli Type
- {15,2,24}
- Vertices, edges, …
- 15, 15, 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
9-fold
10-fold
12-fold
15-fold
18-fold
20-fold
24-fold
30-fold
36-fold
40-fold
60-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);; s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);; s2 := (17,18)(19,20)(21,24)(22,26)(23,25)(27,30)(28,32)(29,31)(34,37)(35,36)(38,39);; s3 := (16,22)(17,19)(18,28)(20,23)(21,25)(24,34)(26,29)(27,31)(30,38)(32,35)(33,36)(37,39);; 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*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(39)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15); s1 := Sym(39)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14); s2 := Sym(39)!(17,18)(19,20)(21,24)(22,26)(23,25)(27,30)(28,32)(29,31)(34,37)(35,36)(38,39); s3 := Sym(39)!(16,22)(17,19)(18,28)(20,23)(21,25)(24,34)(26,29)(27,31)(30,38)(32,35)(33,36)(37,39); poly := sub<Sym(39)|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*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 >;