Overview
- Group
- SmallGroup(1920,239473)
- Rank
- 4
- Schläfli Type
- {2,8,15}
- Vertices, edges, …
- 2, 32, 240, 60
- 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 := (1,2);; s1 := ( 3,11)( 4,12)( 5,13)( 6,14)( 7,18)( 8,17)( 9,16)(10,15)(19,27)(20,28)(21,29)(22,30)(23,34)(24,33)(25,32)(26,31)(35,43)(36,44)(37,45)(38,46)(39,50)(40,49)(41,48)(42,47)(51,59)(52,60)(53,61)(54,62)(55,66)(56,65)(57,64)(58,63)(67,75)(68,76)(69,77)(70,78)(71,82)(72,81)(73,80)(74,79);; s2 := ( 5, 6)( 7,12)( 8,11)( 9,13)(10,14)(17,18)(19,67)(20,68)(21,70)(22,69)(23,76)(24,75)(25,77)(26,78)(27,72)(28,71)(29,73)(30,74)(31,79)(32,80)(33,82)(34,81)(35,51)(36,52)(37,54)(38,53)(39,60)(40,59)(41,61)(42,62)(43,56)(44,55)(45,57)(46,58)(47,63)(48,64)(49,66)(50,65);; s3 := ( 3,27)( 4,30)( 5,29)( 6,28)( 7,25)( 8,24)( 9,23)(10,26)(11,19)(12,22)(13,21)(14,20)(15,31)(16,34)(17,33)(18,32)(35,75)(36,78)(37,77)(38,76)(39,73)(40,72)(41,71)(42,74)(43,67)(44,70)(45,69)(46,68)(47,79)(48,82)(49,81)(50,80)(51,59)(52,62)(53,61)(54,60)(55,57)(64,66);; 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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(82)!(1,2); s1 := Sym(82)!( 3,11)( 4,12)( 5,13)( 6,14)( 7,18)( 8,17)( 9,16)(10,15)(19,27)(20,28)(21,29)(22,30)(23,34)(24,33)(25,32)(26,31)(35,43)(36,44)(37,45)(38,46)(39,50)(40,49)(41,48)(42,47)(51,59)(52,60)(53,61)(54,62)(55,66)(56,65)(57,64)(58,63)(67,75)(68,76)(69,77)(70,78)(71,82)(72,81)(73,80)(74,79); s2 := Sym(82)!( 5, 6)( 7,12)( 8,11)( 9,13)(10,14)(17,18)(19,67)(20,68)(21,70)(22,69)(23,76)(24,75)(25,77)(26,78)(27,72)(28,71)(29,73)(30,74)(31,79)(32,80)(33,82)(34,81)(35,51)(36,52)(37,54)(38,53)(39,60)(40,59)(41,61)(42,62)(43,56)(44,55)(45,57)(46,58)(47,63)(48,64)(49,66)(50,65); s3 := Sym(82)!( 3,27)( 4,30)( 5,29)( 6,28)( 7,25)( 8,24)( 9,23)(10,26)(11,19)(12,22)(13,21)(14,20)(15,31)(16,34)(17,33)(18,32)(35,75)(36,78)(37,77)(38,76)(39,73)(40,72)(41,71)(42,74)(43,67)(44,70)(45,69)(46,68)(47,79)(48,82)(49,81)(50,80)(51,59)(52,62)(53,61)(54,60)(55,57)(64,66); 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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;