Overview
- Group
- SmallGroup(1296,3492)
- Rank
- 4
- Schläfli Type
- {2,12,9}
- Vertices, edges, …
- 2, 36, 162, 27
- 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)( 7, 8)(10,11)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(19,29)(20,28);; s2 := ( 3, 4)( 6,22)( 7,21)( 8,23)( 9,13)(10,12)(11,14)(15,28)(16,27)(17,29)(18,19)(24,25);; s3 := ( 4,21)( 5,12)( 6, 9)( 7,27)( 8,18)(10,24)(11,15)(13,23)(16,29)(17,20)(19,26)(25,28);; 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*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s3*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(29)!(1,2); s1 := Sym(29)!( 4, 5)( 7, 8)(10,11)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(19,29)(20,28); s2 := Sym(29)!( 3, 4)( 6,22)( 7,21)( 8,23)( 9,13)(10,12)(11,14)(15,28)(16,27)(17,29)(18,19)(24,25); s3 := Sym(29)!( 4,21)( 5,12)( 6, 9)( 7,27)( 8,18)(10,24)(11,15)(13,23)(16,29)(17,20)(19,26)(25,28); 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*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s3*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2*s3 >;