Overview
- Group
- SmallGroup(1728,30790)
- Rank
- 6
- Schläfli Type
- {3,2,2,18,4}
- Vertices, edges, …
- 3, 3, 2, 18, 36, 4
- Order of s0s1s2s3s4s5
- 36
- 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
3-fold
4-fold
6-fold
9-fold
12-fold
18-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := (4,5);; s3 := ( 7, 8)( 9,13)(10,12)(11,14)(16,17)(18,22)(19,21)(20,23)(25,26)(27,31)(28,30)(29,32)(34,35)(36,40)(37,39)(38,41);; s4 := ( 6, 9)( 7,11)( 8,10)(12,13)(15,18)(16,20)(17,19)(21,22)(24,36)(25,38)(26,37)(27,33)(28,35)(29,34)(30,40)(31,39)(32,41);; s5 := ( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40)(23,41);; 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*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,
s0*s1*s0*s1*s0*s1, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(41)!(2,3); s1 := Sym(41)!(1,2); s2 := Sym(41)!(4,5); s3 := Sym(41)!( 7, 8)( 9,13)(10,12)(11,14)(16,17)(18,22)(19,21)(20,23)(25,26)(27,31)(28,30)(29,32)(34,35)(36,40)(37,39)(38,41); s4 := Sym(41)!( 6, 9)( 7,11)( 8,10)(12,13)(15,18)(16,20)(17,19)(21,22)(24,36)(25,38)(26,37)(27,33)(28,35)(29,34)(30,40)(31,39)(32,41); s5 := Sym(41)!( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40)(23,41); poly := sub<Sym(41)|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*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, s0*s1*s0*s1*s0*s1, s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;