Overview
- Group
- SmallGroup(1728,47870)
- Rank
- 4
- Schläfli Type
- {2,12,12}
- Vertices, edges, …
- 2, 36, 216, 36
- 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 := (1,2);; s1 := ( 3, 5)( 4, 6)( 7,13)( 8,14)( 9,11)(10,12)(15,29)(16,30)(17,27)(18,28)(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,31)(26,32);; s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,19)(16,21)(17,20)(18,22)(24,25)(27,31)(28,33)(29,32)(30,34)(36,37);; s3 := ( 4, 6)( 7,15)( 8,18)( 9,17)(10,16)(11,27)(12,30)(13,29)(14,28)(20,22)(23,31)(24,34)(25,33)(26,32)(36,38);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3,
s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(38)!(1,2); s1 := Sym(38)!( 3, 5)( 4, 6)( 7,13)( 8,14)( 9,11)(10,12)(15,29)(16,30)(17,27)(18,28)(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,31)(26,32); s2 := Sym(38)!( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,19)(16,21)(17,20)(18,22)(24,25)(27,31)(28,33)(29,32)(30,34)(36,37); s3 := Sym(38)!( 4, 6)( 7,15)( 8,18)( 9,17)(10,16)(11,27)(12,30)(13,29)(14,28)(20,22)(23,31)(24,34)(25,33)(26,32)(36,38); 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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3, s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 >;