Overview
- Group
- SmallGroup(768,201205)
- Rank
- 4
- Schläfli Type
- {4,8,12}
- Vertices, edges, …
- 4, 16, 48, 12
- Order of s0s1s2s3
- 24
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
16-fold
24-fold
32-fold
48-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := (25,34)(26,35)(27,36)(28,31)(29,32)(30,33)(37,46)(38,47)(39,48)(40,43)(41,44)(42,45);; s1 := ( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,35)(12,36)(13,40)(14,41)(15,42)(16,37)(17,38)(18,39)(19,46)(20,47)(21,48)(22,43)(23,44)(24,45);; s2 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17)(19,22)(20,24)(21,23)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,43)(32,45)(33,44)(34,46)(35,48)(36,47);; s3 := ( 1, 3)( 4, 6)( 7, 9)(10,12)(13,18)(14,17)(15,16)(19,24)(20,23)(21,22)(25,27)(28,30)(31,33)(34,36)(37,42)(38,41)(39,40)(43,48)(44,47)(45,46);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(48)!(25,34)(26,35)(27,36)(28,31)(29,32)(30,33)(37,46)(38,47)(39,48)(40,43)(41,44)(42,45); s1 := Sym(48)!( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,35)(12,36)(13,40)(14,41)(15,42)(16,37)(17,38)(18,39)(19,46)(20,47)(21,48)(22,43)(23,44)(24,45); s2 := Sym(48)!( 2, 3)( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17)(19,22)(20,24)(21,23)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,43)(32,45)(33,44)(34,46)(35,48)(36,47); s3 := Sym(48)!( 1, 3)( 4, 6)( 7, 9)(10,12)(13,18)(14,17)(15,16)(19,24)(20,23)(21,22)(25,27)(28,30)(31,33)(34,36)(37,42)(38,41)(39,40)(43,48)(44,47)(45,46); poly := sub<Sym(48)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References
None.
to this polytope.