Overview
- Group
- SmallGroup(1728,47874)
- Rank
- 4
- Schläfli Type
- {12,6,2}
- Vertices, edges, …
- 72, 216, 36, 2
- 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, 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 := ( 1,17)( 2,19)( 3,18)( 4,20)( 5,13)( 6,15)( 7,14)( 8,16)( 9,21)(10,23)(11,22)(12,24)(25,29)(26,31)(27,30)(28,32)(34,35);; s2 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16)(17,21)(18,24)(19,23)(20,22)(26,28)(29,33)(30,36)(31,35)(32,34);; 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*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)!( 1,17)( 2,19)( 3,18)( 4,20)( 5,13)( 6,15)( 7,14)( 8,16)( 9,21)(10,23)(11,22)(12,24)(25,29)(26,31)(27,30)(28,32)(34,35); s2 := Sym(38)!( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16)(17,21)(18,24)(19,23)(20,22)(26,28)(29,33)(30,36)(31,35)(32,34); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1 >;