Overview
- Group
- SmallGroup(1000,106)
- Rank
- 4
- Schläfli Type
- {2,5,10}
- Vertices, edges, …
- 2, 25, 125, 50
- Order of s0s1s2s3
- 10
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
5-fold
25-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 8,23)( 9,24)(10,25)(11,26)(12,27)(13,18)(14,19)(15,20)(16,21)(17,22);; s2 := ( 3, 9)( 4,10)( 5,11)( 6,12)( 7, 8)(13,25)(14,26)(15,27)(16,23)(17,24);; s3 := ( 4, 7)( 5, 6)( 8,23)( 9,27)(10,26)(11,25)(12,24)(13,18)(14,22)(15,21)(16,20)(17,19);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(27)!(1,2); s1 := Sym(27)!( 8,23)( 9,24)(10,25)(11,26)(12,27)(13,18)(14,19)(15,20)(16,21)(17,22); s2 := Sym(27)!( 3, 9)( 4,10)( 5,11)( 6,12)( 7, 8)(13,25)(14,26)(15,27)(16,23)(17,24); s3 := Sym(27)!( 4, 7)( 5, 6)( 8,23)( 9,27)(10,26)(11,25)(12,24)(13,18)(14,22)(15,21)(16,20)(17,19); poly := sub<Sym(27)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s1*s2 >;