Overview
- Group
- SmallGroup(432,522)
- Rank
- 5
- Schläfli Type
- {3,2,9,4}
- Vertices, edges, …
- 3, 3, 9, 18, 4
- Order of s0s1s2s3s4
- 9
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 4, 5)( 6, 9)( 7, 8)(10,18)(11,17)(12,19)(13,15)(14,16)(20,26)(21,27)(22,24)(23,25)(28,34)(29,35)(30,32)(31,33)(36,39)(37,38);; s3 := ( 4, 8)( 5, 6)( 7,15)( 9,11)(10,12)(13,24)(14,25)(16,18)(17,20)(19,21)(22,32)(23,33)(26,28)(27,29)(30,34)(31,38)(35,36)(37,39);; s4 := ( 4,18)( 5,10)( 6,12)( 9,19)(13,23)(15,25)(20,29)(22,31)(24,33)(26,35)(28,36)(34,39);; 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*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,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(39)!(2,3); s1 := Sym(39)!(1,2); s2 := Sym(39)!( 4, 5)( 6, 9)( 7, 8)(10,18)(11,17)(12,19)(13,15)(14,16)(20,26)(21,27)(22,24)(23,25)(28,34)(29,35)(30,32)(31,33)(36,39)(37,38); s3 := Sym(39)!( 4, 8)( 5, 6)( 7,15)( 9,11)(10,12)(13,24)(14,25)(16,18)(17,20)(19,21)(22,32)(23,33)(26,28)(27,29)(30,34)(31,38)(35,36)(37,39); s4 := Sym(39)!( 4,18)( 5,10)( 6,12)( 9,19)(13,23)(15,25)(20,29)(22,31)(24,33)(26,35)(28,36)(34,39); poly := sub<Sym(39)|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*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, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;