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