Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,15,4}

Atlas Canonical Name {2,4,15,4}*960

Overview

Group
SmallGroup(960,11381)
Rank
5
Schläfli Type
{2,4,15,4}
Vertices, edges, …
2, 4, 30, 30, 4
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

Covers minimal covers in bold

2-fold

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 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,67)(20,69)(21,68)(22,70)(23,75)(24,77)(25,76)(26,78)(27,71)(28,73)(29,72)(30,74)(31,79)(32,81)(33,80)(34,82)(35,51)(36,53)(37,52)(38,54)(39,59)(40,61)(41,60)(42,62)(43,55)(44,57)(45,56)(46,58)(47,63)(48,65)(49,64)(50,66);;
s3 := ( 3,19)( 4,20)( 5,22)( 6,21)( 7,31)( 8,32)( 9,34)(10,33)(11,27)(12,28)(13,30)(14,29)(15,23)(16,24)(17,26)(18,25)(35,67)(36,68)(37,70)(38,69)(39,79)(40,80)(41,82)(42,81)(43,75)(44,76)(45,78)(46,77)(47,71)(48,72)(49,74)(50,73)(53,54)(55,63)(56,64)(57,66)(58,65)(61,62);;
s4 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37)(39,42)(40,41)(43,46)(44,45)(47,50)(48,49)(51,54)(52,53)(55,58)(56,57)(59,62)(60,61)(63,66)(64,65)(67,70)(68,69)(71,74)(72,73)(75,78)(76,77)(79,82)(80,81);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, s4*s3*s2*s4*s3*s4*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)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,67)(20,69)(21,68)(22,70)(23,75)(24,77)(25,76)(26,78)(27,71)(28,73)(29,72)(30,74)(31,79)(32,81)(33,80)(34,82)(35,51)(36,53)(37,52)(38,54)(39,59)(40,61)(41,60)(42,62)(43,55)(44,57)(45,56)(46,58)(47,63)(48,65)(49,64)(50,66);
s3 := Sym(82)!( 3,19)( 4,20)( 5,22)( 6,21)( 7,31)( 8,32)( 9,34)(10,33)(11,27)(12,28)(13,30)(14,29)(15,23)(16,24)(17,26)(18,25)(35,67)(36,68)(37,70)(38,69)(39,79)(40,80)(41,82)(42,81)(43,75)(44,76)(45,78)(46,77)(47,71)(48,72)(49,74)(50,73)(53,54)(55,63)(56,64)(57,66)(58,65)(61,62);
s4 := Sym(82)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37)(39,42)(40,41)(43,46)(44,45)(47,50)(48,49)(51,54)(52,53)(55,58)(56,57)(59,62)(60,61)(63,66)(64,65)(67,70)(68,69)(71,74)(72,73)(75,78)(76,77)(79,82)(80,81);
poly := sub<Sym(82)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s1*s2, 
s4*s3*s2*s4*s3*s4*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 >;