Overview
- Group
- SmallGroup(1728,47874)
- Rank
- 4
- Schläfli Type
- {2,6,12}
- Vertices, edges, …
- 2, 36, 216, 72
- Order of s0s1s2s3
- 6
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
4-fold
6-fold
9-fold
12-fold
18-fold
24-fold
36-fold
72-fold
108-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)(28,29)(31,35)(32,37)(33,36)(34,38);; s2 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14)(15,31)(16,32)(17,34)(18,33)(19,27)(20,28)(21,30)(22,29)(23,35)(24,36)(25,38)(26,37);; s3 := ( 3,18)( 4,17)( 5,16)( 6,15)( 7,26)( 8,25)( 9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(27,30)(28,29)(31,38)(32,37)(33,36)(34,35);; 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s3*s2*s1,
s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(38)!(1,2); s1 := Sym(38)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)(28,29)(31,35)(32,37)(33,36)(34,38); s2 := Sym(38)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14)(15,31)(16,32)(17,34)(18,33)(19,27)(20,28)(21,30)(22,29)(23,35)(24,36)(25,38)(26,37); s3 := Sym(38)!( 3,18)( 4,17)( 5,16)( 6,15)( 7,26)( 8,25)( 9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(27,30)(28,29)(31,38)(32,37)(33,36)(34,35); 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2, s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s3*s2*s1, s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s3*s2 >;