Overview
- Group
- SmallGroup(1728,47870)
- Rank
- 4
- Schläfli Type
- {12,12,2}
- Vertices, edges, …
- 36, 216, 36, 2
- Order of s0s1s2s3
- 12
- 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
4-fold
9-fold
12-fold
18-fold
36-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 1, 3)( 2, 4)( 5,11)( 6,12)( 7, 9)( 8,10)(13,27)(14,28)(15,25)(16,26)(17,35)(18,36)(19,33)(20,34)(21,31)(22,32)(23,29)(24,30);; s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)(10,11)(13,17)(14,19)(15,18)(16,20)(22,23)(25,29)(26,31)(27,30)(28,32)(34,35);; s2 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)( 9,25)(10,28)(11,27)(12,26)(18,20)(21,29)(22,32)(23,31)(24,30)(34,36);; s3 := (37,38);; 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*s3*s2*s3,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(38)!( 1, 3)( 2, 4)( 5,11)( 6,12)( 7, 9)( 8,10)(13,27)(14,28)(15,25)(16,26)(17,35)(18,36)(19,33)(20,34)(21,31)(22,32)(23,29)(24,30); s1 := Sym(38)!( 1, 5)( 2, 7)( 3, 6)( 4, 8)(10,11)(13,17)(14,19)(15,18)(16,20)(22,23)(25,29)(26,31)(27,30)(28,32)(34,35); s2 := Sym(38)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)( 9,25)(10,28)(11,27)(12,26)(18,20)(21,29)(22,32)(23,31)(24,30)(34,36); s3 := Sym(38)!(37,38); poly := sub<Sym(38)|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*s3*s2*s3, s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;