Overview
- Group
- SmallGroup(1944,2341)
- Rank
- 3
- Schläfli Type
- {18,6}
- Vertices, edges, …
- 162, 486, 54
- 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
- Self-Petrie
Quotients maximal quotients in bold
3-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*(s2*s1)^2*s0*(s1*s2)^2> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<s0*s2*(s1*s0)^3*s2*(s1*s0)^2*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*s0)^2*s1*s2> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<(s0*s1)^3*(s0*s2*s1)^2*s0*(s1*s2)^2*s1> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2, (s0*s1)^9> of order 6
12 facets
27 vertex figures
- 27 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(10,22)(11,24)(12,23)(13,19)(14,21)(15,20)(16,25)(17,27)(18,26)(29,30)(31,34)(32,36)(33,35)(37,49)(38,51)(39,50)(40,46)(41,48)(42,47)(43,52)(44,54)(45,53)(56,57)(58,61)(59,63)(60,62)(64,76)(65,78)(66,77)(67,73)(68,75)(69,74)(70,79)(71,81)(72,80);; s1 := ( 1,10)( 2,11)( 3,12)( 4,16)( 5,17)( 6,18)( 7,13)( 8,14)( 9,15)(19,22)(20,23)(21,24)(28,66)(29,64)(30,65)(31,72)(32,70)(33,71)(34,69)(35,67)(36,68)(37,57)(38,55)(39,56)(40,63)(41,61)(42,62)(43,60)(44,58)(45,59)(46,78)(47,76)(48,77)(49,75)(50,73)(51,74)(52,81)(53,79)(54,80);; s2 := ( 1,28)( 2,29)( 3,30)( 4,31)( 5,32)( 6,33)( 7,34)( 8,35)( 9,36)(10,37)(11,38)(12,39)(13,40)(14,41)(15,42)(16,43)(17,44)(18,45)(19,46)(20,47)(21,48)(22,49)(23,50)(24,51)(25,52)(26,53)(27,54);; 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,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(81)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(10,22)(11,24)(12,23)(13,19)(14,21)(15,20)(16,25)(17,27)(18,26)(29,30)(31,34)(32,36)(33,35)(37,49)(38,51)(39,50)(40,46)(41,48)(42,47)(43,52)(44,54)(45,53)(56,57)(58,61)(59,63)(60,62)(64,76)(65,78)(66,77)(67,73)(68,75)(69,74)(70,79)(71,81)(72,80); s1 := Sym(81)!( 1,10)( 2,11)( 3,12)( 4,16)( 5,17)( 6,18)( 7,13)( 8,14)( 9,15)(19,22)(20,23)(21,24)(28,66)(29,64)(30,65)(31,72)(32,70)(33,71)(34,69)(35,67)(36,68)(37,57)(38,55)(39,56)(40,63)(41,61)(42,62)(43,60)(44,58)(45,59)(46,78)(47,76)(48,77)(49,75)(50,73)(51,74)(52,81)(53,79)(54,80); s2 := Sym(81)!( 1,28)( 2,29)( 3,30)( 4,31)( 5,32)( 6,33)( 7,34)( 8,35)( 9,36)(10,37)(11,38)(12,39)(13,40)(14,41)(15,42)(16,43)(17,44)(18,45)(19,46)(20,47)(21,48)(22,49)(23,50)(24,51)(25,52)(26,53)(27,54); 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, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.