Overview
- Group
- SmallGroup(1920,239472)
- Rank
- 4
- Schläfli Type
- {2,4,30}
- Vertices, edges, …
- 2, 16, 240, 120
- Order of s0s1s2s3
- 30
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
4-fold
5-fold
8-fold
20-fold
40-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)( 7,15)( 8,16)( 9,17)(10,18)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)(25,33)(26,34)(35,43)(36,44)(37,45)(38,46)(39,47)(40,48)(41,49)(42,50)(51,59)(52,60)(53,61)(54,62)(55,63)(56,64)(57,65)(58,66)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80)(73,81)(74,82);; s2 := ( 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);; s3 := ( 3,19)( 4,21)( 5,20)( 6,22)( 7,31)( 8,33)( 9,32)(10,34)(11,27)(12,29)(13,28)(14,30)(15,23)(16,25)(17,24)(18,26)(35,67)(36,69)(37,68)(38,70)(39,79)(40,81)(41,80)(42,82)(43,75)(44,77)(45,76)(46,78)(47,71)(48,73)(49,72)(50,74)(52,53)(55,63)(56,65)(57,64)(58,66)(60,61);; 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*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2,
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*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)( 7,15)( 8,16)( 9,17)(10,18)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)(25,33)(26,34)(35,43)(36,44)(37,45)(38,46)(39,47)(40,48)(41,49)(42,50)(51,59)(52,60)(53,61)(54,62)(55,63)(56,64)(57,65)(58,66)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80)(73,81)(74,82); s2 := 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); s3 := Sym(82)!( 3,19)( 4,21)( 5,20)( 6,22)( 7,31)( 8,33)( 9,32)(10,34)(11,27)(12,29)(13,28)(14,30)(15,23)(16,25)(17,24)(18,26)(35,67)(36,69)(37,68)(38,70)(39,79)(40,81)(41,80)(42,82)(43,75)(44,77)(45,76)(46,78)(47,71)(48,73)(49,72)(50,74)(52,53)(55,63)(56,65)(57,64)(58,66)(60,61); 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*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2, 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*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 >;