Overview
- Group
- SmallGroup(1920,239473)
- Rank
- 4
- Schläfli Type
- {8,15,2}
- Vertices, edges, …
- 32, 240, 60, 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 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,25)(18,26)(19,27)(20,28)(21,32)(22,31)(23,30)(24,29)(33,41)(34,42)(35,43)(36,44)(37,48)(38,47)(39,46)(40,45)(49,57)(50,58)(51,59)(52,60)(53,64)(54,63)(55,62)(56,61)(65,73)(66,74)(67,75)(68,76)(69,80)(70,79)(71,78)(72,77);; s1 := ( 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);; s2 := ( 1,25)( 2,28)( 3,27)( 4,26)( 5,23)( 6,22)( 7,21)( 8,24)( 9,17)(10,20)(11,19)(12,18)(13,29)(14,32)(15,31)(16,30)(33,73)(34,76)(35,75)(36,74)(37,71)(38,70)(39,69)(40,72)(41,65)(42,68)(43,67)(44,66)(45,77)(46,80)(47,79)(48,78)(49,57)(50,60)(51,59)(52,58)(53,55)(62,64);; 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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(82)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,25)(18,26)(19,27)(20,28)(21,32)(22,31)(23,30)(24,29)(33,41)(34,42)(35,43)(36,44)(37,48)(38,47)(39,46)(40,45)(49,57)(50,58)(51,59)(52,60)(53,64)(54,63)(55,62)(56,61)(65,73)(66,74)(67,75)(68,76)(69,80)(70,79)(71,78)(72,77); s1 := 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); s2 := Sym(82)!( 1,25)( 2,28)( 3,27)( 4,26)( 5,23)( 6,22)( 7,21)( 8,24)( 9,17)(10,20)(11,19)(12,18)(13,29)(14,32)(15,31)(16,30)(33,73)(34,76)(35,75)(36,74)(37,71)(38,70)(39,69)(40,72)(41,65)(42,68)(43,67)(44,66)(45,77)(46,80)(47,79)(48,78)(49,57)(50,60)(51,59)(52,58)(53,55)(62,64); 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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;