Overview
- Group
- SmallGroup(1296,3492)
- Rank
- 4
- Schläfli Type
- {2,9,12}
- Vertices, edges, …
- 2, 27, 162, 36
- Order of s0s1s2s3
- 18
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
27-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 6,21)( 7,23)( 8,22)( 9,12)(10,14)(11,13)(15,27)(16,29)(17,28)(19,20)(25,26);; s2 := ( 3, 6)( 4,24)( 5,15)( 7,21)( 8,12)(10,27)(11,18)(13,26)(14,17)(16,23)(19,29)(22,25);; s3 := ( 6, 9)( 7,10)( 8,11)(12,21)(13,22)(14,23)(15,27)(16,28)(17,29)(18,24)(19,25)(20,26);; 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*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(29)!(1,2); s1 := Sym(29)!( 4, 5)( 6,21)( 7,23)( 8,22)( 9,12)(10,14)(11,13)(15,27)(16,29)(17,28)(19,20)(25,26); s2 := Sym(29)!( 3, 6)( 4,24)( 5,15)( 7,21)( 8,12)(10,27)(11,18)(13,26)(14,17)(16,23)(19,29)(22,25); s3 := Sym(29)!( 6, 9)( 7,10)( 8,11)(12,21)(13,22)(14,23)(15,27)(16,28)(17,29)(18,24)(19,25)(20,26); poly := sub<Sym(29)|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*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s3*s2*s3 >;