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