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