Overview
- Group
- SmallGroup(1728,47847)
- Rank
- 4
- Schläfli Type
- {4,12,3}
- Vertices, edges, …
- 12, 144, 108, 6
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Orientable
- Flat
Quotients maximal quotients in bold
4-fold
9-fold
18-fold
36-fold
72-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)^6> of order 2
4 facets
- 2 of {4,6}*144
- 2 of {4,12}*288
12 vertex figures
- 12 of 2-fold non-regular quotient of {12,3}*144
P/N, where N=<(s0*s1*s2*s1)^2> of order 3
6 facets
- 6 of 3-fold non-regular quotient of {4,12}*288
4 vertex figures
- 4 of {12,3}*144
P/N, where N=<s0*(s1*s2)^3*s1*s0*s2> of order 3
6 facets
- 6 of 3-fold non-regular quotient of {4,12}*288
8 vertex figures
- 2 of {12,3}*144
- 6 of {4,3}*48
P/N, where N=<s0*s1*s2*s1*s0*s2> of order 6
4 facets
- 2 of 3-fold non-regular quotient of {4,6}*144
- 2 of 3-fold non-regular quotient of {4,12}*288
8 vertex figures
- 2 of 2-fold non-regular quotient of {12,3}*144
- 6 of 2-fold non-regular quotient of {4,3}*48
P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*s1*s2*s1*s0*(s1*s2)^3> of order 6
4 facets
- 2 of 3-fold non-regular quotient of {4,6}*144
- 2 of 3-fold non-regular quotient of {4,12}*288
4 vertex figures
- 4 of 2-fold non-regular quotient of {12,3}*144
Representations
Permutation Representation (GAP)
s0 := ( 5,29)( 6,30)( 7,31)( 8,32)( 9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(15,27)(16,28);; s1 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,35)(14,36)(15,33)(16,34)(17,27)(18,28)(19,25)(20,26)(21,31)(22,32)(23,29)(24,30);; s2 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,13)( 6,14)( 7,16)( 8,15)( 9,21)(10,22)(11,24)(12,23)(25,29)(26,30)(27,32)(28,31)(35,36);; s3 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,25)(14,28)(15,27)(16,26)(17,33)(18,36)(19,35)(20,34)(21,29)(22,32)(23,31)(24,30);; 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,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s3*s1*s0*s1*s2*s1*s0*s1*s2*s3*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(36)!( 5,29)( 6,30)( 7,31)( 8,32)( 9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(15,27)(16,28); s1 := Sym(36)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,35)(14,36)(15,33)(16,34)(17,27)(18,28)(19,25)(20,26)(21,31)(22,32)(23,29)(24,30); s2 := Sym(36)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,13)( 6,14)( 7,16)( 8,15)( 9,21)(10,22)(11,24)(12,23)(25,29)(26,30)(27,32)(28,31)(35,36); s3 := Sym(36)!( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,25)(14,28)(15,27)(16,26)(17,33)(18,36)(19,35)(20,34)(21,29)(22,32)(23,31)(24,30); poly := sub<Sym(36)|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, s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s2*s3*s1*s0*s1*s2*s1*s0*s1*s2*s3*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.