Overview
- Group
- SmallGroup(1728,47847)
- Rank
- 4
- Schläfli Type
- {6,12,6}
- Vertices, edges, …
- 8, 72, 72, 9
- Order of s0s1s2s3
- 4
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Non-Orientable
- Flat
Quotients maximal quotients in bold
12-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 7, 8)(11,12)(15,16)(19,20)(23,24)(27,28)(31,32)(35,36);; s1 := ( 2, 4)( 5,29)( 6,32)( 7,31)( 8,30)( 9,21)(10,24)(11,23)(12,22)(13,25)(14,28)(15,27)(16,26)(18,20)(34,36);; s2 := ( 1, 2)( 5, 6)( 9,10)(13,34)(14,33)(15,35)(16,36)(17,26)(18,25)(19,27)(20,28)(21,30)(22,29)(23,31)(24,32);; s3 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,13)( 6,14)( 7,15)( 8,16)( 9,21)(10,22)(11,23)(12,24)(25,29)(26,30)(27,31)(28,32);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(36)!( 3, 4)( 7, 8)(11,12)(15,16)(19,20)(23,24)(27,28)(31,32)(35,36); s1 := Sym(36)!( 2, 4)( 5,29)( 6,32)( 7,31)( 8,30)( 9,21)(10,24)(11,23)(12,22)(13,25)(14,28)(15,27)(16,26)(18,20)(34,36); s2 := Sym(36)!( 1, 2)( 5, 6)( 9,10)(13,34)(14,33)(15,35)(16,36)(17,26)(18,25)(19,27)(20,28)(21,30)(22,29)(23,31)(24,32); s3 := Sym(36)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,13)( 6,14)( 7,15)( 8,16)( 9,21)(10,22)(11,23)(12,24)(25,29)(26,30)(27,31)(28,32); poly := sub<Sym(36)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2, s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 >;
References
None.
to this polytope.