Overview
- Group
- SmallGroup(1344,11527)
- Rank
- 5
- Schläfli Type
- {6,2,4,14}
- Vertices, edges, …
- 6, 6, 4, 28, 14
- Order of s0s1s2s3s4
- 84
- 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
3-fold
4-fold
6-fold
7-fold
8-fold
12-fold
14-fold
21-fold
28-fold
42-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (3,4)(5,6);; s1 := (1,5)(2,3)(4,6);; s2 := ( 8,11)(12,17)(13,18)(19,25)(20,26)(27,31)(28,32);; s3 := ( 7, 8)( 9,13)(10,12)(11,16)(14,20)(15,19)(17,24)(18,23)(21,28)(22,27)(25,30)(26,29)(31,34)(32,33);; s4 := ( 7, 9)( 8,12)(10,14)(11,17)(13,19)(15,21)(16,23)(18,25)(20,27)(24,29)(26,31)(30,33);; 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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(34)!(3,4)(5,6); s1 := Sym(34)!(1,5)(2,3)(4,6); s2 := Sym(34)!( 8,11)(12,17)(13,18)(19,25)(20,26)(27,31)(28,32); s3 := Sym(34)!( 7, 8)( 9,13)(10,12)(11,16)(14,20)(15,19)(17,24)(18,23)(21,28)(22,27)(25,30)(26,29)(31,34)(32,33); s4 := Sym(34)!( 7, 9)( 8,12)(10,14)(11,17)(13,19)(15,21)(16,23)(18,25)(20,27)(24,29)(26,31)(30,33); poly := sub<Sym(34)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;