Overview
- Group
- SmallGroup(1920,238293)
- Rank
- 4
- Schläfli Type
- {6,15,2}
- Vertices, edges, …
- 32, 240, 80, 2
- Order of s0s1s2s3
- 40
- 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
20-fold
40-fold
48-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)(19,20)(21,26)(22,25)(23,27)(24,28)(31,32)(35,36)(37,42)(38,41)(39,43)(40,44)(47,48)(51,52)(53,58)(54,57)(55,59)(56,60)(63,64)(67,68)(69,74)(70,73)(71,75)(72,76)(79,80);; s1 := ( 2, 3)( 5, 8)( 9,16)(10,14)(11,15)(12,13)(17,65)(18,67)(19,66)(20,68)(21,72)(22,70)(23,71)(24,69)(25,80)(26,78)(27,79)(28,77)(29,76)(30,74)(31,75)(32,73)(33,49)(34,51)(35,50)(36,52)(37,56)(38,54)(39,55)(40,53)(41,64)(42,62)(43,63)(44,61)(45,60)(46,58)(47,59)(48,57);; s2 := ( 1,29)( 2,30)( 3,32)( 4,31)( 5,22)( 6,21)( 7,23)( 8,24)( 9,26)(10,25)(11,27)(12,28)(13,17)(14,18)(15,20)(16,19)(33,77)(34,78)(35,80)(36,79)(37,70)(38,69)(39,71)(40,72)(41,74)(42,73)(43,75)(44,76)(45,65)(46,66)(47,68)(48,67)(49,61)(50,62)(51,64)(52,63)(53,54)(57,58);; 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*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(82)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(19,20)(21,26)(22,25)(23,27)(24,28)(31,32)(35,36)(37,42)(38,41)(39,43)(40,44)(47,48)(51,52)(53,58)(54,57)(55,59)(56,60)(63,64)(67,68)(69,74)(70,73)(71,75)(72,76)(79,80); s1 := Sym(82)!( 2, 3)( 5, 8)( 9,16)(10,14)(11,15)(12,13)(17,65)(18,67)(19,66)(20,68)(21,72)(22,70)(23,71)(24,69)(25,80)(26,78)(27,79)(28,77)(29,76)(30,74)(31,75)(32,73)(33,49)(34,51)(35,50)(36,52)(37,56)(38,54)(39,55)(40,53)(41,64)(42,62)(43,63)(44,61)(45,60)(46,58)(47,59)(48,57); s2 := Sym(82)!( 1,29)( 2,30)( 3,32)( 4,31)( 5,22)( 6,21)( 7,23)( 8,24)( 9,26)(10,25)(11,27)(12,28)(13,17)(14,18)(15,20)(16,19)(33,77)(34,78)(35,80)(36,79)(37,70)(38,69)(39,71)(40,72)(41,74)(42,73)(43,75)(44,76)(45,65)(46,66)(47,68)(48,67)(49,61)(50,62)(51,64)(52,63)(53,54)(57,58); 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*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 >;