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