Overview
- Group
- SmallGroup(1296,1858)
- Rank
- 5
- Schläfli Type
- {2,6,9,2}
- Vertices, edges, …
- 2, 18, 81, 27, 2
- 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 := ( 4, 5)( 7, 8)(10,11)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(19,29)(20,28)(31,32)(34,35)(37,38)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)(46,56)(47,55)(58,59)(61,62)(64,65)(66,75)(67,77)(68,76)(69,78)(70,80)(71,79)(72,81)(73,83)(74,82);; s2 := ( 3,12)( 4,13)( 5,14)( 6,18)( 7,19)( 8,20)( 9,15)(10,16)(11,17)(24,27)(25,28)(26,29)(30,69)(31,70)(32,71)(33,66)(34,67)(35,68)(36,72)(37,73)(38,74)(39,60)(40,61)(41,62)(42,57)(43,58)(44,59)(45,63)(46,64)(47,65)(48,78)(49,79)(50,80)(51,75)(52,76)(53,77)(54,81)(55,82)(56,83);; s3 := ( 3,30)( 4,31)( 5,32)( 6,36)( 7,37)( 8,38)( 9,33)(10,34)(11,35)(12,50)(13,48)(14,49)(15,56)(16,54)(17,55)(18,53)(19,51)(20,52)(21,40)(22,41)(23,39)(24,46)(25,47)(26,45)(27,43)(28,44)(29,42)(57,60)(58,61)(59,62)(66,80)(67,78)(68,79)(69,77)(70,75)(71,76)(72,83)(73,81)(74,82);; s4 := (84,85);; 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, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1,
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(85)!(1,2); s1 := Sym(85)!( 4, 5)( 7, 8)(10,11)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(19,29)(20,28)(31,32)(34,35)(37,38)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)(46,56)(47,55)(58,59)(61,62)(64,65)(66,75)(67,77)(68,76)(69,78)(70,80)(71,79)(72,81)(73,83)(74,82); s2 := Sym(85)!( 3,12)( 4,13)( 5,14)( 6,18)( 7,19)( 8,20)( 9,15)(10,16)(11,17)(24,27)(25,28)(26,29)(30,69)(31,70)(32,71)(33,66)(34,67)(35,68)(36,72)(37,73)(38,74)(39,60)(40,61)(41,62)(42,57)(43,58)(44,59)(45,63)(46,64)(47,65)(48,78)(49,79)(50,80)(51,75)(52,76)(53,77)(54,81)(55,82)(56,83); s3 := Sym(85)!( 3,30)( 4,31)( 5,32)( 6,36)( 7,37)( 8,38)( 9,33)(10,34)(11,35)(12,50)(13,48)(14,49)(15,56)(16,54)(17,55)(18,53)(19,51)(20,52)(21,40)(22,41)(23,39)(24,46)(25,47)(26,45)(27,43)(28,44)(29,42)(57,60)(58,61)(59,62)(66,80)(67,78)(68,79)(69,77)(70,75)(71,76)(72,83)(73,81)(74,82); s4 := Sym(85)!(84,85); 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, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;