Overview
- Group
- SmallGroup(1920,238293)
- Rank
- 4
- Schläfli Type
- {2,15,6}
- Vertices, edges, …
- 2, 80, 240, 32
- 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 := (1,2);; s1 := ( 5, 6)( 7,14)( 8,13)( 9,11)(10,12)(15,16)(19,67)(20,68)(21,70)(22,69)(23,78)(24,77)(25,75)(26,76)(27,73)(28,74)(29,72)(30,71)(31,80)(32,79)(33,81)(34,82)(35,51)(36,52)(37,54)(38,53)(39,62)(40,61)(41,59)(42,60)(43,57)(44,58)(45,56)(46,55)(47,64)(48,63)(49,65)(50,66);; s2 := ( 3,19)( 4,21)( 5,20)( 6,22)( 7,26)( 8,24)( 9,25)(10,23)(11,34)(12,32)(13,33)(14,31)(15,30)(16,28)(17,29)(18,27)(35,67)(36,69)(37,68)(38,70)(39,74)(40,72)(41,73)(42,71)(43,82)(44,80)(45,81)(46,79)(47,78)(48,76)(49,77)(50,75)(52,53)(55,58)(59,66)(60,64)(61,65)(62,63);; s3 := ( 3,17)( 4,18)( 5,16)( 6,15)( 7, 8)(13,14)(19,33)(20,34)(21,32)(22,31)(23,24)(29,30)(35,49)(36,50)(37,48)(38,47)(39,40)(45,46)(51,65)(52,66)(53,64)(54,63)(55,56)(61,62)(67,81)(68,82)(69,80)(70,79)(71,72)(77,78);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s1*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(82)!(1,2); s1 := Sym(82)!( 5, 6)( 7,14)( 8,13)( 9,11)(10,12)(15,16)(19,67)(20,68)(21,70)(22,69)(23,78)(24,77)(25,75)(26,76)(27,73)(28,74)(29,72)(30,71)(31,80)(32,79)(33,81)(34,82)(35,51)(36,52)(37,54)(38,53)(39,62)(40,61)(41,59)(42,60)(43,57)(44,58)(45,56)(46,55)(47,64)(48,63)(49,65)(50,66); s2 := Sym(82)!( 3,19)( 4,21)( 5,20)( 6,22)( 7,26)( 8,24)( 9,25)(10,23)(11,34)(12,32)(13,33)(14,31)(15,30)(16,28)(17,29)(18,27)(35,67)(36,69)(37,68)(38,70)(39,74)(40,72)(41,73)(42,71)(43,82)(44,80)(45,81)(46,79)(47,78)(48,76)(49,77)(50,75)(52,53)(55,58)(59,66)(60,64)(61,65)(62,63); s3 := Sym(82)!( 3,17)( 4,18)( 5,16)( 6,15)( 7, 8)(13,14)(19,33)(20,34)(21,32)(22,31)(23,24)(29,30)(35,49)(36,50)(37,48)(38,47)(39,40)(45,46)(51,65)(52,66)(53,64)(54,63)(55,56)(61,62)(67,81)(68,82)(69,80)(70,79)(71,72)(77,78); 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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s1*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3 >;