Overview
- Group
- SmallGroup(864,4673)
- Rank
- 3
- Schläfli Type
- {6,6}
- Vertices, edges, …
- 72, 216, 72
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
3-fold
4-fold
6-fold
9-fold
12-fold
18-fold
24-fold
36-fold
72-fold
108-fold
Covers minimal covers in bold
2-fold
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*s0*(s2*s1)^2)^2> of order 2
36 facets
- 36 of {6}*12
36 vertex figures
- 36 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*(s2*s1)^2> of order 2
36 facets
- 36 of {6}*12
36 vertex figures
- 36 of {6}*12
P/N, where N=<s0*(s1*s2)^2*(s1*s0)^2*s2*s1*s2> of order 2
36 facets
- 36 of {6}*12
36 vertex figures
- 36 of {6}*12
P/N, where N=<s0*(s1*s0*s2)^3*s1*s2> of order 3
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2> of order 3
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^2*s0*(s2*s1)^2*s0*(s1*s2)^2> of order 3
30 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^3, s0*s1*s0*(s2*s1)^2*s0*s2*s1> of order 4
24 facets
24 vertex figures
P/N, where N=<(s0*s1)^3, s0*(s1*s2)^2*(s1*s0)^2*s2*s1*s2> of order 4
24 facets
18 vertex figures
- 18 of {6}*12
P/N, where N=<s1*s0*(s1*s2)^2*s1*s0*s2*s1, (s0*s1)^2*s0*s2*s1*s0*(s2*s1)^2> of order 4
18 facets
- 18 of {6}*12
24 vertex figures
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*(s1*s2)^2, s0*s1*(s2*s1*s0)^3*s1> of order 4
18 facets
- 18 of {6}*12
18 vertex figures
- 18 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*s2> of order 4
18 facets
- 18 of {6}*12
18 vertex figures
- 18 of {6}*12
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2*s1, (s1*s0*s2)^2*s1*s0*(s1*s2)^2> of order 4
18 facets
- 18 of {6}*12
18 vertex figures
- 18 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(26,27)(29,33)(30,35)(31,34)(32,36);; s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,29)(14,30)(15,32)(16,31)(17,25)(18,26)(19,28)(20,27)(21,33)(22,34)(23,36)(24,35);; s2 := ( 1,16)( 2,14)( 3,15)( 4,13)( 5,20)( 6,18)( 7,19)( 8,17)( 9,24)(10,22)(11,23)(12,21)(25,28)(29,32)(33,36);; 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,
s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(36)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(26,27)(29,33)(30,35)(31,34)(32,36); s1 := Sym(36)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,29)(14,30)(15,32)(16,31)(17,25)(18,26)(19,28)(20,27)(21,33)(22,34)(23,36)(24,35); s2 := Sym(36)!( 1,16)( 2,14)( 3,15)( 4,13)( 5,20)( 6,18)( 7,19)( 8,17)( 9,24)(10,22)(11,23)(12,21)(25,28)(29,32)(33,36); poly := sub<Sym(36)|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, s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.