Overview
- Group
- SmallGroup(1152,155790)
- Rank
- 4
- Schläfli Type
- {3,12,4}
- Vertices, edges, …
- 6, 72, 96, 8
- Order of s0s1s2s3
- 6
- Order of s0s1s2s3s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
4-fold
6-fold
12-fold
16-fold
24-fold
48-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=<(s2*s3)^2> of order 2
4 facets
- 4 of {3,12}*144
6 vertex figures
- 4 of 2-fold non-regular quotient of {12,4}*192a
- 2 of {12,4}*96a
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2> of order 2
8 facets
- 8 of 2-fold non-regular quotient of {3,12}*144
3 vertex figures
- 3 of {12,4}*192a
P/N, where N=<(s2*s3)^2, s0*s1*s2*s1*s0*(s2*s1)^2> of order 4
4 facets
- 4 of 2-fold non-regular quotient of {3,12}*144
3 vertex figures
- 2 of 2-fold non-regular quotient of {12,4}*192a
- 1 of {12,4}*96a
P/N, where N=<(s2*s3)^2, s0*s1*s2*s1*s0*(s2*s1)^2*s2> of order 4
4 facets
- 4 of 2-fold non-regular quotient of {3,12}*144
4 vertex figures
- 2 of 2-fold non-regular quotient of {12,4}*192a
- 2 of {6,4}*48a
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)( 5,29)( 6,32)( 7,31)( 8,30)( 9,25)(10,28)(11,27)(12,26)(13,21)(14,24)(15,23)(16,22)(34,36)(37,45)(38,48)(39,47)(40,46)(42,44);; s2 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9,13)(10,14)(11,15)(12,16)(17,37)(18,38)(19,39)(20,40)(21,33)(22,34)(23,35)(24,36)(25,45)(26,46)(27,47)(28,48)(29,41)(30,42)(31,43)(32,44);; s3 := ( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(21,22)(23,24)(25,27)(26,28)(29,32)(30,31)(37,38)(39,40)(41,43)(42,44)(45,48)(46,47);; 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,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s3*s2*s1*s2*s0*s1*s2*s3*s2*s1,
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*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)(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)( 5,29)( 6,32)( 7,31)( 8,30)( 9,25)(10,28)(11,27)(12,26)(13,21)(14,24)(15,23)(16,22)(34,36)(37,45)(38,48)(39,47)(40,46)(42,44); s2 := Sym(48)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9,13)(10,14)(11,15)(12,16)(17,37)(18,38)(19,39)(20,40)(21,33)(22,34)(23,35)(24,36)(25,45)(26,46)(27,47)(28,48)(29,41)(30,42)(31,43)(32,44); s3 := Sym(48)!( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(21,22)(23,24)(25,27)(26,28)(29,32)(30,31)(37,38)(39,40)(41,43)(42,44)(45,48)(46,47); 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, s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s3*s2*s1*s2*s0*s1*s2*s3*s2*s1, s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.