Overview
- Group
- SmallGroup(1296,2908)
- Rank
- 3
- Schläfli Type
- {18,4}
- Vertices, edges, …
- 162, 324, 36
- Order of s0s1s2
- 36
- 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
9-fold
18-fold
27-fold
36-fold
54-fold
81-fold
108-fold
162-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)^3*s2*(s1*s0)^2*s1*s2> of order 2
18 facets
- 18 of {18}*36
81 vertex figures
- 81 of {4}*8
P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 3
12 facets
- 12 of {18}*36
54 vertex figures
- 54 of {4}*8
P/N, where N=<s0*s1*s0*s2*(s1*s0)^3*s2*s1*s0*s2*s1*s2> of order 3
12 facets
- 12 of {18}*36
54 vertex figures
- 54 of {4}*8
P/N, where N=<(s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1> of order 3
12 facets
- 12 of {18}*36
54 vertex figures
- 54 of {4}*8
P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1)^9> of order 4
12 facets
45 vertex figures
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, (s0*s1)^6*s0*s2*(s1*s0)^2*s1*s2> of order 6
9 facets
27 vertex figures
- 27 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*(s2*s1*s0)^2> of order 6
6 facets
- 6 of {18}*36
36 vertex figures
P/N, where N=<(s0*s1)^4*s0*s2*s1*s0*s1*s2, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1> of order 9
4 facets
- 4 of {18}*36
18 vertex figures
- 18 of {4}*8
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 8)( 5, 7)( 6, 9)(10,19)(11,21)(12,20)(13,26)(14,25)(15,27)(16,23)(17,22)(18,24)(28,55)(29,57)(30,56)(31,62)(32,61)(33,63)(34,59)(35,58)(36,60)(37,73)(38,75)(39,74)(40,80)(41,79)(42,81)(43,77)(44,76)(45,78)(46,64)(47,66)(48,65)(49,71)(50,70)(51,72)(52,68)(53,67)(54,69);; s1 := ( 1,31)( 2,33)( 3,32)( 4,28)( 5,30)( 6,29)( 7,35)( 8,34)( 9,36)(10,40)(11,42)(12,41)(13,37)(14,39)(15,38)(16,44)(17,43)(18,45)(19,49)(20,51)(21,50)(22,46)(23,48)(24,47)(25,53)(26,52)(27,54)(55,58)(56,60)(57,59)(61,62)(64,67)(65,69)(66,68)(70,71)(73,76)(74,78)(75,77)(79,80);; s2 := (10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,55)(20,56)(21,57)(22,58)(23,59)(24,60)(25,61)(26,62)(27,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72);; 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,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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, 8)( 5, 7)( 6, 9)(10,19)(11,21)(12,20)(13,26)(14,25)(15,27)(16,23)(17,22)(18,24)(28,55)(29,57)(30,56)(31,62)(32,61)(33,63)(34,59)(35,58)(36,60)(37,73)(38,75)(39,74)(40,80)(41,79)(42,81)(43,77)(44,76)(45,78)(46,64)(47,66)(48,65)(49,71)(50,70)(51,72)(52,68)(53,67)(54,69); s1 := Sym(81)!( 1,31)( 2,33)( 3,32)( 4,28)( 5,30)( 6,29)( 7,35)( 8,34)( 9,36)(10,40)(11,42)(12,41)(13,37)(14,39)(15,38)(16,44)(17,43)(18,45)(19,49)(20,51)(21,50)(22,46)(23,48)(24,47)(25,53)(26,52)(27,54)(55,58)(56,60)(57,59)(61,62)(64,67)(65,69)(66,68)(70,71)(73,76)(74,78)(75,77)(79,80); s2 := Sym(81)!(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,55)(20,56)(21,57)(22,58)(23,59)(24,60)(25,61)(26,62)(27,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72); 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, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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.