Overview
- Group
- SmallGroup(1296,1858)
- Rank
- 5
- Schläfli Type
- {2,2,6,9}
- Vertices, edges, …
- 2, 2, 18, 81, 27
- Order of s0s1s2s3s4
- 18
- 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
9-fold
27-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := ( 6, 7)( 9,10)(12,13)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)(20,29)(21,31)(22,30)(33,34)(36,37)(39,40)(41,50)(42,52)(43,51)(44,53)(45,55)(46,54)(47,56)(48,58)(49,57)(60,61)(63,64)(66,67)(68,77)(69,79)(70,78)(71,80)(72,82)(73,81)(74,83)(75,85)(76,84);; s3 := ( 5,14)( 6,15)( 7,16)( 8,20)( 9,21)(10,22)(11,17)(12,18)(13,19)(26,29)(27,30)(28,31)(32,71)(33,72)(34,73)(35,68)(36,69)(37,70)(38,74)(39,75)(40,76)(41,62)(42,63)(43,64)(44,59)(45,60)(46,61)(47,65)(48,66)(49,67)(50,80)(51,81)(52,82)(53,77)(54,78)(55,79)(56,83)(57,84)(58,85);; s4 := ( 5,32)( 6,33)( 7,34)( 8,38)( 9,39)(10,40)(11,35)(12,36)(13,37)(14,52)(15,50)(16,51)(17,58)(18,56)(19,57)(20,55)(21,53)(22,54)(23,42)(24,43)(25,41)(26,48)(27,49)(28,47)(29,45)(30,46)(31,44)(59,62)(60,63)(61,64)(68,82)(69,80)(70,81)(71,79)(72,77)(73,78)(74,85)(75,83)(76,84);; 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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s4*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s4*s3*s2,
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(85)!(1,2); s1 := Sym(85)!(3,4); s2 := Sym(85)!( 6, 7)( 9,10)(12,13)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)(20,29)(21,31)(22,30)(33,34)(36,37)(39,40)(41,50)(42,52)(43,51)(44,53)(45,55)(46,54)(47,56)(48,58)(49,57)(60,61)(63,64)(66,67)(68,77)(69,79)(70,78)(71,80)(72,82)(73,81)(74,83)(75,85)(76,84); s3 := Sym(85)!( 5,14)( 6,15)( 7,16)( 8,20)( 9,21)(10,22)(11,17)(12,18)(13,19)(26,29)(27,30)(28,31)(32,71)(33,72)(34,73)(35,68)(36,69)(37,70)(38,74)(39,75)(40,76)(41,62)(42,63)(43,64)(44,59)(45,60)(46,61)(47,65)(48,66)(49,67)(50,80)(51,81)(52,82)(53,77)(54,78)(55,79)(56,83)(57,84)(58,85); s4 := Sym(85)!( 5,32)( 6,33)( 7,34)( 8,38)( 9,39)(10,40)(11,35)(12,36)(13,37)(14,52)(15,50)(16,51)(17,58)(18,56)(19,57)(20,55)(21,53)(22,54)(23,42)(24,43)(25,41)(26,48)(27,49)(28,47)(29,45)(30,46)(31,44)(59,62)(60,63)(61,64)(68,82)(69,80)(70,81)(71,79)(72,77)(73,78)(74,85)(75,83)(76,84); poly := sub<Sym(85)|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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, s4*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s4*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;