Overview
- Group
- SmallGroup(1920,240507)
- Rank
- 4
- Schläfli Type
- {10,4,4}
- Vertices, edges, …
- 60, 120, 48, 4
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-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)^5> of order 2
4 facets
- 4 of 2-fold non-regular quotient of {10,4}*480a
30 vertex figures
- 30 of {4,4}*32
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2> of order 3
4 facets
- 4 of 3-fold non-regular quotient of {10,4}*480a
20 vertex figures
- 20 of {4,4}*32
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s0> of order 5
4 facets
- 4 of 5-fold non-regular quotient of {10,4}*480a
12 vertex figures
- 12 of {4,4}*32
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5);; s1 := ( 1, 2)( 3, 4)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);; s2 := ( 2, 3)( 6,22)( 7,23)( 8,24)( 9,25)(10,27)(11,26)(12,29)(13,28)(14,32)(15,33)(16,30)(17,31)(18,37)(19,36)(20,35)(21,34);; s3 := ( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(11,19)(12,20)(13,21)(22,30)(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(29,37);; 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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(37)!(2,3)(4,5); s1 := Sym(37)!( 1, 2)( 3, 4)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37); s2 := Sym(37)!( 2, 3)( 6,22)( 7,23)( 8,24)( 9,25)(10,27)(11,26)(12,29)(13,28)(14,32)(15,33)(16,30)(17,31)(18,37)(19,36)(20,35)(21,34); s3 := Sym(37)!( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(11,19)(12,20)(13,21)(22,30)(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(29,37); poly := sub<Sym(37)|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, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2 >;
References
None.
to this polytope.