Overview
- Group
- SmallGroup(324,40)
- Rank
- 3
- Schläfli Type
- {6,18}
- Vertices, edges, …
- 9, 81, 27
- Order of s0s1s2
- 9
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
Quotients maximal quotients in bold
3-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 4, 8)( 5, 9)( 6, 7)(10,19)(11,20)(12,21)(13,26)(14,27)(15,25)(16,24)(17,22)(18,23)(31,35)(32,36)(33,34)(37,46)(38,47)(39,48)(40,53)(41,54)(42,52)(43,51)(44,49)(45,50)(58,62)(59,63)(60,61)(64,73)(65,74)(66,75)(67,80)(68,81)(69,79)(70,78)(71,76)(72,77);; s1 := ( 1,10)( 2,12)( 3,11)( 4,13)( 5,15)( 6,14)( 7,16)( 8,18)( 9,17)(20,21)(23,24)(26,27)(28,65)(29,64)(30,66)(31,68)(32,67)(33,69)(34,71)(35,70)(36,72)(37,56)(38,55)(39,57)(40,59)(41,58)(42,60)(43,62)(44,61)(45,63)(46,74)(47,73)(48,75)(49,77)(50,76)(51,78)(52,80)(53,79)(54,81);; s2 := ( 1,28)( 2,30)( 3,29)( 4,34)( 5,36)( 6,35)( 7,31)( 8,33)( 9,32)(10,40)(11,42)(12,41)(13,37)(14,39)(15,38)(16,43)(17,45)(18,44)(19,53)(20,52)(21,54)(22,50)(23,49)(24,51)(25,47)(26,46)(27,48)(55,56)(58,62)(59,61)(60,63)(64,68)(65,67)(66,69)(70,71)(73,81)(74,80)(75,79)(76,78);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(81)!( 4, 8)( 5, 9)( 6, 7)(10,19)(11,20)(12,21)(13,26)(14,27)(15,25)(16,24)(17,22)(18,23)(31,35)(32,36)(33,34)(37,46)(38,47)(39,48)(40,53)(41,54)(42,52)(43,51)(44,49)(45,50)(58,62)(59,63)(60,61)(64,73)(65,74)(66,75)(67,80)(68,81)(69,79)(70,78)(71,76)(72,77); s1 := Sym(81)!( 1,10)( 2,12)( 3,11)( 4,13)( 5,15)( 6,14)( 7,16)( 8,18)( 9,17)(20,21)(23,24)(26,27)(28,65)(29,64)(30,66)(31,68)(32,67)(33,69)(34,71)(35,70)(36,72)(37,56)(38,55)(39,57)(40,59)(41,58)(42,60)(43,62)(44,61)(45,63)(46,74)(47,73)(48,75)(49,77)(50,76)(51,78)(52,80)(53,79)(54,81); s2 := Sym(81)!( 1,28)( 2,30)( 3,29)( 4,34)( 5,36)( 6,35)( 7,31)( 8,33)( 9,32)(10,40)(11,42)(12,41)(13,37)(14,39)(15,38)(16,43)(17,45)(18,44)(19,53)(20,52)(21,54)(22,50)(23,49)(24,51)(25,47)(26,46)(27,48)(55,56)(58,62)(59,61)(60,63)(64,68)(65,67)(66,69)(70,71)(73,81)(74,80)(75,79)(76,78); poly := sub<Sym(81)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0 >;
References
None.
to this polytope.