Overview
- Group
- SmallGroup(1152,155790)
- Rank
- 3
- Schläfli Type
- {12,6}
- Vertices, edges, …
- 96, 288, 48
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 12
- 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*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 2
28 facets
48 vertex figures
- 48 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s0> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<s1*s0*(s2*s1)^2*s0*s1*s0*(s2*s1)^2> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<s1*(s0*(s2*s1)^2)^2*s0*s2*s1*s2> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<(s0*s1)^6, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
16 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s1*s2)^3, s1*s0*(s2*s1)^2*(s0*s1)^2*s2> of order 4
12 facets
- 12 of {12}*24
30 vertex figures
P/N, where N=<(s0*s1)^3*s2*s1*s0*s1*s2*s1, (s0*s1)^2*(s2*s1*s0*s1)^2> of order 4
18 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2, s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 4
16 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*(s1*s2)^2*(s1*s0)^2*s2*s1*s2, s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 4
14 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2*s1, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, (s0*s1*s0*(s2*s1)^2)^2> of order 4
14 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*s0*(s2*s1)^2*s0*s1*s0*(s2*s1)^2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*s0*(s2*s1)^2*s0*s1*s0*(s2*s1)^2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2, (s1*s0)^2*s1*s2*s1*s0*s1*s2*s1> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 4
14 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s0*s1*s0*(s2*s1)^2*s0*s1*s2*s1*s0*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2, s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 4
14 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s1*s2)^3, (s0*s1)^2*(s2*s1)^2*s0*s2*s1*s0> of order 4
12 facets
- 12 of {12}*24
36 vertex figures
P/N, where N=<s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s1*s2)^3, (s0*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s0> of order 4
12 facets
- 12 of {12}*24
30 vertex figures
P/N, where N=<s1*s0*(s2*s1)^2*(s0*s1)^2*s2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<s1*s0*(s2*s1)^2*s0*s1*s0*(s2*s1)^2, s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 4
14 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2, s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 4
14 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s2*(s1*s0)^2*(s1*s2)^2*s1> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s1*s2)^3, (s0*s1)^6> of order 8
8 facets
18 vertex figures
P/N, where N=<(s0*s1)^3*s2*s1*s0*s1*s2*s1, (s0*s1)^2*(s2*s1*s0*s1)^2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 8
9 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 8
7 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2, (s1*s0)^2*s1*s2*s1*s0*s1*s2*s1, s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 8
6 facets
- 6 of {12}*24
12 vertex figures
- 12 of {6}*12
P/N, where N=<s1*s0*(s2*s1)^2*s0*(s1*s2)^2, (s0*s1)^6> of order 8
8 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<s0*s1*s2*(s1*s0)^2*(s1*s2)^2*s1, s0*(s1*s2)^2*(s1*s0)^2*s1*s2*s1> of order 8
6 facets
- 6 of {12}*24
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2, (s1*s0)^2*s1*s2*s1*s0*s1*s2*s1, (s0*s2*s1)^2*s0*(s1*s2)^2*s1> of order 8
6 facets
- 6 of {12}*24
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^6, s0*(s1*s2)^2*(s1*s0)^2*s2*s1*s2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 8
8 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^6, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 8
10 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s1*s2)^3, (s1*s0)^2*s2*s1*s0*s1*s2, (s1*s0)^2*s1*s2*s1*s0*s1*s2*s1> of order 8
6 facets
- 6 of {12}*24
18 vertex figures
P/N, where N=<(s1*s2)^3, s1*s0*(s2*s1)^2*(s0*s1)^2*s2, (s0*s1)^2*(s2*s1)^2*s0*s2*s1*s0> of order 8
6 facets
- 6 of {12}*24
18 vertex figures
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^2*(s2*s1*s0*s1)^2, s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 8
8 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s1*s2)^3, (s0*s1)^2*(s2*s1)^2*s0*s2*s1*s0, s0*(s1*s2)^2*(s1*s0)^2*s1*s2*s1> of order 8
6 facets
- 6 of {12}*24
18 vertex figures
P/N, where N=<(s0*s1)^6, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8
8 facets
12 vertex figures
- 12 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,33)(26,34)(27,35)(28,36)(29,37)(30,38)(31,39)(32,40);; s1 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,22)( 6,21)( 7,23)( 8,24)( 9,32)(10,31)(11,29)(12,30)(13,27)(14,28)(15,26)(16,25)(35,36)(37,38)(41,48)(42,47)(43,45)(44,46);; s2 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(17,33)(18,36)(19,35)(20,34)(21,45)(22,48)(23,47)(24,46)(25,41)(26,44)(27,43)(28,42)(29,37)(30,40)(31,39)(32,38);; 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*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(48)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,33)(26,34)(27,35)(28,36)(29,37)(30,38)(31,39)(32,40); s1 := Sym(48)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,22)( 6,21)( 7,23)( 8,24)( 9,32)(10,31)(11,29)(12,30)(13,27)(14,28)(15,26)(16,25)(35,36)(37,38)(41,48)(42,47)(43,45)(44,46); s2 := Sym(48)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(17,33)(18,36)(19,35)(20,34)(21,45)(22,48)(23,47)(24,46)(25,41)(26,44)(27,43)(28,42)(29,37)(30,40)(31,39)(32,38); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*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 >;
References
None.
to this polytope.