Overview
- Group
- SmallGroup(1792,1035859)
- Rank
- 5
- Schläfli Type
- {14,2,4,8}
- Vertices, edges, …
- 14, 14, 4, 16, 8
- Order of s0s1s2s3s4
- 56
- 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
7-fold
8-fold
14-fold
16-fold
28-fold
56-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);; s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);; s2 := (16,18)(17,20)(24,27)(26,29);; s3 := (15,16)(17,19)(18,21)(20,23)(22,24)(25,27)(26,28)(29,30);; s4 := (16,17)(18,20)(19,22)(23,25)(24,26)(27,29);; 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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(30)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14); s1 := Sym(30)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14); s2 := Sym(30)!(16,18)(17,20)(24,27)(26,29); s3 := Sym(30)!(15,16)(17,19)(18,21)(20,23)(22,24)(25,27)(26,28)(29,30); s4 := Sym(30)!(16,17)(18,20)(19,22)(23,25)(24,26)(27,29); poly := sub<Sym(30)|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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;