Overview
- Group
- SmallGroup(1920,239473)
- Rank
- 4
- Schläfli Type
- {15,8,2}
- Vertices, edges, …
- 60, 240, 32, 2
- Order of s0s1s2s3
- 30
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
4-fold
5-fold
8-fold
16-fold
20-fold
40-fold
48-fold
80-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,65)(18,66)(19,68)(20,67)(21,74)(22,73)(23,75)(24,76)(25,70)(26,69)(27,71)(28,72)(29,77)(30,78)(31,80)(32,79)(33,49)(34,50)(35,52)(36,51)(37,58)(38,57)(39,59)(40,60)(41,54)(42,53)(43,55)(44,56)(45,61)(46,62)(47,64)(48,63);; s1 := ( 1,17)( 2,19)( 3,18)( 4,20)( 5,21)( 6,23)( 7,22)( 8,24)( 9,31)(10,29)(11,32)(12,30)(13,26)(14,28)(15,25)(16,27)(33,65)(34,67)(35,66)(36,68)(37,69)(38,71)(39,70)(40,72)(41,79)(42,77)(43,80)(44,78)(45,74)(46,76)(47,73)(48,75)(50,51)(54,55)(57,63)(58,61)(59,64)(60,62);; s2 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5, 9)( 6,10)( 7,11)( 8,12)(17,29)(18,30)(19,31)(20,32)(21,25)(22,26)(23,27)(24,28)(33,45)(34,46)(35,47)(36,48)(37,41)(38,42)(39,43)(40,44)(49,61)(50,62)(51,63)(52,64)(53,57)(54,58)(55,59)(56,60)(65,77)(66,78)(67,79)(68,80)(69,73)(70,74)(71,75)(72,76);; s3 := (81,82);; 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,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(82)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,65)(18,66)(19,68)(20,67)(21,74)(22,73)(23,75)(24,76)(25,70)(26,69)(27,71)(28,72)(29,77)(30,78)(31,80)(32,79)(33,49)(34,50)(35,52)(36,51)(37,58)(38,57)(39,59)(40,60)(41,54)(42,53)(43,55)(44,56)(45,61)(46,62)(47,64)(48,63); s1 := Sym(82)!( 1,17)( 2,19)( 3,18)( 4,20)( 5,21)( 6,23)( 7,22)( 8,24)( 9,31)(10,29)(11,32)(12,30)(13,26)(14,28)(15,25)(16,27)(33,65)(34,67)(35,66)(36,68)(37,69)(38,71)(39,70)(40,72)(41,79)(42,77)(43,80)(44,78)(45,74)(46,76)(47,73)(48,75)(50,51)(54,55)(57,63)(58,61)(59,64)(60,62); s2 := Sym(82)!( 1,13)( 2,14)( 3,15)( 4,16)( 5, 9)( 6,10)( 7,11)( 8,12)(17,29)(18,30)(19,31)(20,32)(21,25)(22,26)(23,27)(24,28)(33,45)(34,46)(35,47)(36,48)(37,41)(38,42)(39,43)(40,44)(49,61)(50,62)(51,63)(52,64)(53,57)(54,58)(55,59)(56,60)(65,77)(66,78)(67,79)(68,80)(69,73)(70,74)(71,75)(72,76); s3 := Sym(82)!(81,82); poly := sub<Sym(82)|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, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;