Overview
- Group
- SmallGroup(1944,2346)
- Rank
- 3
- Schläfli Type
- {6,6}
- Vertices, edges, …
- 162, 486, 162
- Order of s0s1s2
- 18
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
3-fold
6-fold
9-fold
18-fold
27-fold
54-fold
81-fold
162-fold
243-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 3
54 facets
- 54 of {6}*12
54 vertex figures
- 54 of {6}*12
P/N, where N=<s1*s2*s1*(s0*(s2*s1)^2)^2*s2> of order 3
54 facets
- 54 of {6}*12
54 vertex figures
- 54 of {6}*12
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*(s2*s1)^2*s0*s1*s2> of order 3
54 facets
- 54 of {6}*12
60 vertex figures
P/N, where N=<(s1*s2*s1*s0)^2*(s1*s2)^2> of order 3
54 facets
- 54 of {6}*12
54 vertex figures
- 54 of {6}*12
P/N, where N=<s0*s1*(s2*s1*s0)^2*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 3
54 facets
- 54 of {6}*12
54 vertex figures
- 54 of {6}*12
P/N, where N=<(s0*s1)^3, (s1*s0*s2)^2*s1*s0*(s1*s2)^2> of order 6
36 facets
27 vertex figures
- 27 of {6}*12
P/N, where N=<s1*s0*(s1*s2)^2*s1*s0*s2*s1, s0*s1*s0*s2*(s1*s0)^2*(s1*s2)^2> of order 6
27 facets
- 27 of {6}*12
30 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)(10,20)(11,19)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(29,30)(32,33)(35,36)(37,47)(38,46)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)(56,57)(59,60)(62,63)(64,74)(65,73)(66,75)(67,77)(68,76)(69,78)(70,80)(71,79)(72,81);; s1 := ( 1,13)( 2,15)( 3,14)( 4,18)( 5,17)( 6,16)( 7,11)( 8,10)( 9,12)(20,21)(22,24)(25,26)(28,67)(29,69)(30,68)(31,72)(32,71)(33,70)(34,65)(35,64)(36,66)(37,62)(38,61)(39,63)(40,55)(41,57)(42,56)(43,60)(44,59)(45,58)(46,73)(47,75)(48,74)(49,78)(50,77)(51,76)(52,80)(53,79)(54,81);; s2 := ( 1,28)( 2,29)( 3,30)( 4,34)( 5,35)( 6,36)( 7,31)( 8,32)( 9,33)(10,37)(11,38)(12,39)(13,43)(14,44)(15,45)(16,40)(17,41)(18,42)(19,46)(20,47)(21,48)(22,52)(23,53)(24,54)(25,49)(26,50)(27,51)(58,61)(59,62)(60,63)(67,70)(68,71)(69,72)(76,79)(77,80)(78,81);; 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(81)!( 2, 3)( 5, 6)( 8, 9)(10,20)(11,19)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(29,30)(32,33)(35,36)(37,47)(38,46)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)(56,57)(59,60)(62,63)(64,74)(65,73)(66,75)(67,77)(68,76)(69,78)(70,80)(71,79)(72,81); s1 := Sym(81)!( 1,13)( 2,15)( 3,14)( 4,18)( 5,17)( 6,16)( 7,11)( 8,10)( 9,12)(20,21)(22,24)(25,26)(28,67)(29,69)(30,68)(31,72)(32,71)(33,70)(34,65)(35,64)(36,66)(37,62)(38,61)(39,63)(40,55)(41,57)(42,56)(43,60)(44,59)(45,58)(46,73)(47,75)(48,74)(49,78)(50,77)(51,76)(52,80)(53,79)(54,81); s2 := Sym(81)!( 1,28)( 2,29)( 3,30)( 4,34)( 5,35)( 6,36)( 7,31)( 8,32)( 9,33)(10,37)(11,38)(12,39)(13,43)(14,44)(15,45)(16,40)(17,41)(18,42)(19,46)(20,47)(21,48)(22,52)(23,53)(24,54)(25,49)(26,50)(27,51)(58,61)(59,62)(60,63)(67,70)(68,71)(69,72)(76,79)(77,80)(78,81); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References
None.
to this polytope.