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