Overview
- Group
- SmallGroup(1944,2344)
- Rank
- 3
- Schläfli Type
- {18,6}
- Vertices, edges, …
- 162, 486, 54
- Order of s0s1s2
- 6
- 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
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<(s1*s2*s1*s0)^2*(s1*s2)^2> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<(s0*(s1*s2)^2*s1)^2> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, s1*s0*(s1*s2)^2*(s1*s0)^2*(s2*s1)^2> of order 6
12 facets
27 vertex figures
- 27 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^3*s2*s1*s0*s1*s2*s1> of order 9
6 facets
- 6 of {18}*36
18 vertex figures
- 18 of {6}*12
P/N, where N=<(s0*(s2*s1)^2)^2, s1*s0*s1*s2*s1*s0*(s1*s2)^3> of order 9
6 facets
- 6 of {18}*36
18 vertex figures
- 18 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)(17,27)(18,26)(29,30)(32,33)(35,36)(37,46)(38,48)(39,47)(40,49)(41,51)(42,50)(43,52)(44,54)(45,53)(56,57)(59,60)(62,63)(64,73)(65,75)(66,74)(67,76)(68,78)(69,77)(70,79)(71,81)(72,80);; s1 := ( 1,13)( 2,15)( 3,14)( 4,17)( 5,16)( 6,18)( 7,12)( 8,11)( 9,10)(19,20)(22,24)(26,27)(28,67)(29,69)(30,68)(31,71)(32,70)(33,72)(34,66)(35,65)(36,64)(37,63)(38,62)(39,61)(40,55)(41,57)(42,56)(43,59)(44,58)(45,60)(46,74)(47,73)(48,75)(49,78)(50,77)(51,76)(52,79)(53,81)(54,80);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(81)!( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)(17,27)(18,26)(29,30)(32,33)(35,36)(37,46)(38,48)(39,47)(40,49)(41,51)(42,50)(43,52)(44,54)(45,53)(56,57)(59,60)(62,63)(64,73)(65,75)(66,74)(67,76)(68,78)(69,77)(70,79)(71,81)(72,80); s1 := Sym(81)!( 1,13)( 2,15)( 3,14)( 4,17)( 5,16)( 6,18)( 7,12)( 8,11)( 9,10)(19,20)(22,24)(26,27)(28,67)(29,69)(30,68)(31,71)(32,70)(33,72)(34,66)(35,65)(36,64)(37,63)(38,62)(39,61)(40,55)(41,57)(42,56)(43,59)(44,58)(45,60)(46,74)(47,73)(48,75)(49,78)(50,77)(51,76)(52,79)(53,81)(54,80); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.