Overview
- Group
- SmallGroup(1728,46114)
- Rank
- 5
- Schläfli Type
- {2,6,9,2}
- Vertices, edges, …
- 2, 24, 108, 36, 2
- Order of s0s1s2s3s4
- 36
- 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)(16,17)(20,21)(24,25)(28,29)(32,33)(36,37);; s2 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(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)( 4,16)( 5,17)( 6,15)( 7,26)( 8,24)( 9,25)(10,23)(11,22)(12,20)(13,21)(14,19)(27,34)(28,32)(29,33)(30,31)(35,38);; 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*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*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)(16,17)(20,21)(24,25)(28,29)(32,33)(36,37); s2 := Sym(40)!( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(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(40)!( 3,18)( 4,16)( 5,17)( 6,15)( 7,26)( 8,24)( 9,25)(10,23)(11,22)(12,20)(13,21)(14,19)(27,34)(28,32)(29,33)(30,31)(35,38); 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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 >;