Overview
- Group
- SmallGroup(1152,155790)
- Rank
- 3
- Schläfli Type
- {6,6}
- Vertices, edges, …
- 96, 288, 96
- 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
Quotients maximal quotients in bold
3-fold
4-fold
6-fold
8-fold
12-fold
16-fold
24-fold
32-fold
48-fold
96-fold
144-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*s0*s1*(s2*s1*s0)^2*s1*s2*s1> of order 2
48 facets
- 48 of {6}*12
48 vertex figures
- 48 of {6}*12
P/N, where N=<s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2> of order 2
48 facets
- 48 of {6}*12
52 vertex figures
P/N, where N=<(s1*s2*s1*s0)^2*(s1*s2)^2> of order 2
48 facets
- 48 of {6}*12
48 vertex figures
- 48 of {6}*12
P/N, where N=<s1*s0*s1*s2*(s1*s0)^2*(s1*s2)^2> of order 2
48 facets
- 48 of {6}*12
48 vertex figures
- 48 of {6}*12
P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*(s2*s1*s0)^2*s1*s2*s1*s0*s2*s1, s0*s2*s1*s0*s1*(s2*s1*s0)^2*s1*s2*s1> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s1*s2*s1*s0)^2*(s1*s2)^2, (s0*s1*s0*(s2*s1)^2)^2> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*(s1*s0*s2)^2*s1*s2> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, ((s1*s0)^2*s1*s2)^2> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<((s1*s0)^2*s1*s2)^2, s1*s0*s1*s2*(s1*s0)^2*(s1*s2)^2> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1*s2*s1)^3, s1*s0*s1*s2*(s1*s0)^2*(s1*s2)^2> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s1*s2*s1> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s1*s2*s1*s0)^2*(s1*s2)^2, (s0*s1)^2*s0*(s2*s1)^2*s0*s1*s0*s2*s1> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<s1*s0*s1*s2*s1*s0*(s1*s2)^3, (s1*s2*s1*s0)^2*(s1*s2)^2> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*s2*s1*s2> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2, ((s1*s0)^2*s1*s2)^2> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^3, (s0*s1*s2*s1)^3> of order 4
30 facets
26 vertex figures
P/N, where N=<s1*s0*(s1*s2)^2*s1*s0*s2*s1, ((s1*s0)^2*s1*s2)^2> of order 4
24 facets
- 24 of {6}*12
28 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s0*(s2*s1)^2)^2> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^2*s2*s1*s0*(s1*s2)^2*s1, s0*s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s1> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2*s1*s2*s1> of order 4
24 facets
- 24 of {6}*12
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^3, s0*s2*(s1*s0)^2*s1*s2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2> of order 8
18 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^2*s2*s1*s0*(s1*s2)^2*s1, (s0*s1*s2*s1)^3, s1*s0*s1*s2*(s1*s0)^2*(s1*s2)^2> of order 8
12 facets
- 12 of {6}*12
12 vertex figures
- 12 of {6}*12
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2, s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 8
12 facets
- 12 of {6}*12
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^3, s0*s2*(s1*s0)^2*s1*s2, s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 8
18 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s1*s2*s1, s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2> of order 8
12 facets
- 12 of {6}*12
12 vertex figures
- 12 of {6}*12
P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2, ((s1*s0)^2*s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^2> of order 8
12 facets
- 12 of {6}*12
12 vertex figures
- 12 of {6}*12
P/N, where N=<s0*(s1*s2)^2*(s1*s0)^2*s2*s1, (s1*s0)^2*s2*s1*s0*(s2*s1)^2> of order 8
12 facets
- 12 of {6}*12
12 vertex figures
- 12 of {6}*12
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, ((s1*s0)^2*s1*s2)^2, (s1*s2)^2*(s1*s0*s1*s2)^2> of order 8
12 facets
- 12 of {6}*12
12 vertex figures
- 12 of {6}*12
P/N, where N=<s1*s0*(s1*s2)^2*s1*s0*s2*s1, ((s1*s0)^2*s1*s2)^2, s1*s0*s1*s2*(s1*s0)^2*(s1*s2)^2> of order 8
12 facets
- 12 of {6}*12
14 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s0*(s2*s1)^2)^2, s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 8
12 facets
- 12 of {6}*12
12 vertex figures
- 12 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*s1> of order 8
12 facets
- 12 of {6}*12
14 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s2*s1> of order 12
8 facets
- 8 of {6}*12
12 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*s2> of order 12
8 facets
- 8 of {6}*12
12 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(17,33)(18,34)(19,36)(20,35)(21,37)(22,38)(23,40)(24,39)(25,45)(26,46)(27,48)(28,47)(29,41)(30,42)(31,44)(32,43);; s1 := ( 1,17)( 2,20)( 3,19)( 4,18)( 5,32)( 6,29)( 7,30)( 8,31)( 9,27)(10,26)(11,25)(12,28)(13,22)(14,23)(15,24)(16,21)(34,36)(37,48)(38,45)(39,46)(40,47)(41,43);; s2 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(15,16)(17,21)(18,22)(19,24)(20,23)(27,28)(31,32)(33,37)(34,38)(35,40)(36,39)(43,44)(47,48);; 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,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(48)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(17,33)(18,34)(19,36)(20,35)(21,37)(22,38)(23,40)(24,39)(25,45)(26,46)(27,48)(28,47)(29,41)(30,42)(31,44)(32,43); s1 := Sym(48)!( 1,17)( 2,20)( 3,19)( 4,18)( 5,32)( 6,29)( 7,30)( 8,31)( 9,27)(10,26)(11,25)(12,28)(13,22)(14,23)(15,24)(16,21)(34,36)(37,48)(38,45)(39,46)(40,47)(41,43); s2 := Sym(48)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(15,16)(17,21)(18,22)(19,24)(20,23)(27,28)(31,32)(33,37)(34,38)(35,40)(36,39)(43,44)(47,48); poly := sub<Sym(48)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.