Overview
- Group
- SmallGroup(1440,5924)
- Rank
- 6
- Schläfli Type
- {3,2,2,6,10}
- Vertices, edges, …
- 3, 3, 2, 6, 30, 10
- Order of s0s1s2s3s4s5
- 30
- Order of s0s1s2s3s4s5s4s3s2s1
- 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);; s1 := (1,2);; s2 := (4,5);; s3 := ( 8, 9)(12,13)(16,18)(17,19)(22,24)(23,25)(28,30)(29,31)(32,34)(33,35);; s4 := ( 6, 8)( 7,12)(10,17)(11,16)(14,23)(15,22)(18,19)(20,29)(21,28)(24,25)(26,33)(27,32)(30,31)(34,35);; s5 := ( 6,14)( 7,10)( 8,22)( 9,24)(11,26)(12,16)(13,18)(15,20)(17,32)(19,34)(21,27)(23,28)(25,30)(29,33)(31,35);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s0*s1*s0*s1*s0*s1, s3*s4*s5*s4*s3*s4*s5*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(35)!(2,3); s1 := Sym(35)!(1,2); s2 := Sym(35)!(4,5); s3 := Sym(35)!( 8, 9)(12,13)(16,18)(17,19)(22,24)(23,25)(28,30)(29,31)(32,34)(33,35); s4 := Sym(35)!( 6, 8)( 7,12)(10,17)(11,16)(14,23)(15,22)(18,19)(20,29)(21,28)(24,25)(26,33)(27,32)(30,31)(34,35); s5 := Sym(35)!( 6,14)( 7,10)( 8,22)( 9,24)(11,26)(12,16)(13,18)(15,20)(17,32)(19,34)(21,27)(23,28)(25,30)(29,33)(31,35); poly := sub<Sym(35)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, s3*s4*s5*s4*s3*s4*s5*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;