Overview
- Group
- SmallGroup(1200,1006)
- Rank
- 5
- Schläfli Type
- {5,2,10,6}
- Vertices, edges, …
- 5, 5, 10, 30, 6
- Order of s0s1s2s3s4
- 30
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
6-fold
10-fold
15-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5);; s1 := (1,2)(3,4);; s2 := (10,11)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35);; s3 := ( 6,10)( 7,14)( 8,18)( 9,16)(11,20)(12,24)(13,22)(15,26)(17,30)(19,28)(23,34)(25,32)(29,31)(33,35);; s4 := ( 6,12)( 7, 8)( 9,13)(10,22)(11,23)(14,16)(15,17)(18,24)(19,25)(20,32)(21,33)(26,28)(27,29)(30,34)(31,35);; 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*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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(35)!(2,3)(4,5); s1 := Sym(35)!(1,2)(3,4); s2 := Sym(35)!(10,11)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35); s3 := Sym(35)!( 6,10)( 7,14)( 8,18)( 9,16)(11,20)(12,24)(13,22)(15,26)(17,30)(19,28)(23,34)(25,32)(29,31)(33,35); s4 := Sym(35)!( 6,12)( 7, 8)( 9,13)(10,22)(11,23)(14,16)(15,17)(18,24)(19,25)(20,32)(21,33)(26,28)(27,29)(30,34)(31,35); poly := sub<Sym(35)|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*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;