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