Overview
- Group
- SmallGroup(1152,155791)
- Rank
- 3
- Schläfli Type
- {24,6}
- Vertices, edges, …
- 96, 288, 24
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 24
- 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=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 2
16 facets
48 vertex figures
- 48 of {6}*12
P/N, where N=<(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 2
12 facets
- 12 of {24}*48
48 vertex figures
- 48 of {6}*12
P/N, where N=<(s1*s0)^2*s2*s1*s0*(s2*s1)^2> of order 2
12 facets
- 12 of {24}*48
48 vertex figures
- 48 of {6}*12
P/N, where N=<(s1*s0)^2*s1*s2*s1*s0*s1*s2*s1> of order 2
12 facets
- 12 of {24}*48
48 vertex figures
- 48 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
8 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2, (s1*s0)^2*s2*s1*s0*(s2*s1)^2> of order 4
8 facets
24 vertex figures
- 24 of {6}*12
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
8 facets
24 vertex figures
- 24 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,14)( 6,13)( 7,16)( 8,15)(17,41)(18,42)(19,43)(20,44)(21,46)(22,45)(23,48)(24,47)(25,33)(26,34)(27,35)(28,36)(29,38)(30,37)(31,40)(32,39);; s1 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,22)( 6,21)( 7,23)( 8,24)( 9,29)(10,30)(11,32)(12,31)(13,25)(14,26)(15,28)(16,27)(35,36)(37,38)(41,45)(42,46)(43,48)(44,47);; s2 := ( 1, 9)( 2,12)( 3,11)( 4,10)( 6, 8)(13,15)(17,41)(18,44)(19,43)(20,42)(21,37)(22,40)(23,39)(24,38)(25,33)(26,36)(27,35)(28,34)(29,47)(30,46)(31,45)(32,48);; 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, s1*s2*s1*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,
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*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(48)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,14)( 6,13)( 7,16)( 8,15)(17,41)(18,42)(19,43)(20,44)(21,46)(22,45)(23,48)(24,47)(25,33)(26,34)(27,35)(28,36)(29,38)(30,37)(31,40)(32,39); s1 := Sym(48)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,22)( 6,21)( 7,23)( 8,24)( 9,29)(10,30)(11,32)(12,31)(13,25)(14,26)(15,28)(16,27)(35,36)(37,38)(41,45)(42,46)(43,48)(44,47); s2 := Sym(48)!( 1, 9)( 2,12)( 3,11)( 4,10)( 6, 8)(13,15)(17,41)(18,44)(19,43)(20,42)(21,37)(22,40)(23,39)(24,38)(25,33)(26,36)(27,35)(28,34)(29,47)(30,46)(31,45)(32,48); 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, s1*s2*s1*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, 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*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1 >;
References
None.
to this polytope.