Overview
- Group
- SmallGroup(1280,1083341)
- Rank
- 6
- Schläfli Type
- {2,2,2,8,10}
- Vertices, edges, …
- 2, 2, 2, 8, 40, 10
- Order of s0s1s2s3s4s5
- 40
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
5-fold
8-fold
10-fold
20-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := (5,6);; s3 := (17,22)(18,23)(19,24)(20,25)(21,26)(27,42)(28,43)(29,44)(30,45)(31,46)(32,37)(33,38)(34,39)(35,40)(36,41);; s4 := ( 7,27)( 8,31)( 9,30)(10,29)(11,28)(12,32)(13,36)(14,35)(15,34)(16,33)(17,42)(18,46)(19,45)(20,44)(21,43)(22,37)(23,41)(24,40)(25,39)(26,38);; s5 := ( 7, 8)( 9,11)(12,13)(14,16)(17,18)(19,21)(22,23)(24,26)(27,28)(29,31)(32,33)(34,36)(37,38)(39,41)(42,43)(44,46);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(46)!(1,2); s1 := Sym(46)!(3,4); s2 := Sym(46)!(5,6); s3 := Sym(46)!(17,22)(18,23)(19,24)(20,25)(21,26)(27,42)(28,43)(29,44)(30,45)(31,46)(32,37)(33,38)(34,39)(35,40)(36,41); s4 := Sym(46)!( 7,27)( 8,31)( 9,30)(10,29)(11,28)(12,32)(13,36)(14,35)(15,34)(16,33)(17,42)(18,46)(19,45)(20,44)(21,43)(22,37)(23,41)(24,40)(25,39)(26,38); s5 := Sym(46)!( 7, 8)( 9,11)(12,13)(14,16)(17,18)(19,21)(22,23)(24,26)(27,28)(29,31)(32,33)(34,36)(37,38)(39,41)(42,43)(44,46); poly := sub<Sym(46)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;