Overview
- Group
- SmallGroup(480,1169)
- Rank
- 4
- Schläfli Type
- {4,2,30}
- Vertices, edges, …
- 4, 4, 30, 30
- Order of s0s1s2s3
- 60
- 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
10-fold
12-fold
15-fold
20-fold
30-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2)(3,4);; s2 := ( 7, 8)( 9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,24)(22,23)(25,26)(27,30)(28,29)(31,34)(32,33);; s3 := ( 5,21)( 6,15)( 7,13)( 8,23)( 9,11)(10,31)(12,17)(14,27)(16,25)(18,33)(19,22)(20,32)(24,29)(26,28)(30,34);; 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, 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(34)!(2,3); s1 := Sym(34)!(1,2)(3,4); s2 := Sym(34)!( 7, 8)( 9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,24)(22,23)(25,26)(27,30)(28,29)(31,34)(32,33); s3 := Sym(34)!( 5,21)( 6,15)( 7,13)( 8,23)( 9,11)(10,31)(12,17)(14,27)(16,25)(18,33)(19,22)(20,32)(24,29)(26,28)(30,34); 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, 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;