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