Part of the Atlas of Small Regular Polytopes

Polytope of Type {30,4,2}

Atlas Canonical Name {30,4,2}*1920a

Overview

Group
SmallGroup(1920,239472)
Rank
4
Schläfli Type
{30,4,2}
Vertices, edges, …
120, 240, 16, 2
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 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,65)(18,66)(19,68)(20,67)(21,73)(22,74)(23,76)(24,75)(25,69)(26,70)(27,72)(28,71)(29,77)(30,78)(31,80)(32,79)(33,49)(34,50)(35,52)(36,51)(37,57)(38,58)(39,60)(40,59)(41,53)(42,54)(43,56)(44,55)(45,61)(46,62)(47,64)(48,63);;
s1 := ( 1,17)( 2,20)( 3,19)( 4,18)( 5,23)( 6,22)( 7,21)( 8,24)( 9,30)(10,31)(11,32)(12,29)(13,28)(14,25)(15,26)(16,27)(33,65)(34,68)(35,67)(36,66)(37,71)(38,70)(39,69)(40,72)(41,78)(42,79)(43,80)(44,77)(45,76)(46,73)(47,74)(48,75)(50,52)(53,55)(57,62)(58,63)(59,64)(60,61);;
s2 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5, 9)( 6,10)( 7,11)( 8,12)(17,29)(18,30)(19,31)(20,32)(21,25)(22,26)(23,27)(24,28)(33,45)(34,46)(35,47)(36,48)(37,41)(38,42)(39,43)(40,44)(49,61)(50,62)(51,63)(52,64)(53,57)(54,58)(55,59)(56,60)(65,77)(66,78)(67,79)(68,80)(69,73)(70,74)(71,75)(72,76);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(82)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,65)(18,66)(19,68)(20,67)(21,73)(22,74)(23,76)(24,75)(25,69)(26,70)(27,72)(28,71)(29,77)(30,78)(31,80)(32,79)(33,49)(34,50)(35,52)(36,51)(37,57)(38,58)(39,60)(40,59)(41,53)(42,54)(43,56)(44,55)(45,61)(46,62)(47,64)(48,63);
s1 := Sym(82)!( 1,17)( 2,20)( 3,19)( 4,18)( 5,23)( 6,22)( 7,21)( 8,24)( 9,30)(10,31)(11,32)(12,29)(13,28)(14,25)(15,26)(16,27)(33,65)(34,68)(35,67)(36,66)(37,71)(38,70)(39,69)(40,72)(41,78)(42,79)(43,80)(44,77)(45,76)(46,73)(47,74)(48,75)(50,52)(53,55)(57,62)(58,63)(59,64)(60,61);
s2 := Sym(82)!( 1,13)( 2,14)( 3,15)( 4,16)( 5, 9)( 6,10)( 7,11)( 8,12)(17,29)(18,30)(19,31)(20,32)(21,25)(22,26)(23,27)(24,28)(33,45)(34,46)(35,47)(36,48)(37,41)(38,42)(39,43)(40,44)(49,61)(50,62)(51,63)(52,64)(53,57)(54,58)(55,59)(56,60)(65,77)(66,78)(67,79)(68,80)(69,73)(70,74)(71,75)(72,76);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;