Overview
- Group
- SmallGroup(1728,46116)
- Rank
- 5
- Schläfli Type
- {2,3,6,2}
- Vertices, edges, …
- 2, 36, 108, 72, 2
- Order of s0s1s2s3s4
- 12
- Order of s0s1s2s3s4s3s2s1
- 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
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 := ( 4, 5)( 8, 9)(12,13)(15,27)(16,29)(17,28)(18,30)(19,31)(20,33)(21,32)(22,34)(23,35)(24,37)(25,36)(26,38);; s2 := ( 3,19)( 4,22)( 5,21)( 6,20)( 7,23)( 8,26)( 9,25)(10,24)(11,15)(12,18)(13,17)(14,16)(28,30)(32,34)(36,38);; s3 := ( 3, 6)( 7,14)( 8,12)( 9,13)(10,11)(15,18)(19,26)(20,24)(21,25)(22,23)(27,30)(31,38)(32,36)(33,37)(34,35);; s4 := (39,40);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(40)!(1,2); s1 := Sym(40)!( 4, 5)( 8, 9)(12,13)(15,27)(16,29)(17,28)(18,30)(19,31)(20,33)(21,32)(22,34)(23,35)(24,37)(25,36)(26,38); s2 := Sym(40)!( 3,19)( 4,22)( 5,21)( 6,20)( 7,23)( 8,26)( 9,25)(10,24)(11,15)(12,18)(13,17)(14,16)(28,30)(32,34)(36,38); s3 := Sym(40)!( 3, 6)( 7,14)( 8,12)( 9,13)(10,11)(15,18)(19,26)(20,24)(21,25)(22,23)(27,30)(31,38)(32,36)(33,37)(34,35); s4 := Sym(40)!(39,40); poly := sub<Sym(40)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;