Overview
- Group
- SmallGroup(1728,47874)
- Rank
- 6
- Schläfli Type
- {4,3,2,3,6}
- Vertices, edges, …
- 8, 12, 6, 3, 9, 6
- Order of s0s1s2s3s4s5
- 6
- Order of s0s1s2s3s4s5s4s3s2s1
- 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
12-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (4,6);; s1 := (3,4)(5,6);; s2 := (1,3)(2,5);; s3 := ( 8, 9)(10,11)(12,15)(13,14);; s4 := ( 7,12)( 8,10)( 9,14)(11,13);; s5 := (10,11)(12,13)(14,15);; 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, 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, s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(15)!(4,6); s1 := Sym(15)!(3,4)(5,6); s2 := Sym(15)!(1,3)(2,5); s3 := Sym(15)!( 8, 9)(10,11)(12,15)(13,14); s4 := Sym(15)!( 7,12)( 8,10)( 9,14)(11,13); s5 := Sym(15)!(10,11)(12,13)(14,15); poly := sub<Sym(15)|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, 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, s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4 >;