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