Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,2,4,12}

Atlas Canonical Name {10,2,4,12}*1920c

Overview

Group
SmallGroup(1920,240141)
Rank
5
Schläfli Type
{10,2,4,12}
Vertices, edges, …
10, 10, 4, 24, 12
Order of s0s1s2s3s4
60
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

2-fold

4-fold

5-fold

8-fold

10-fold

20-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (11,31)(12,23)(13,20)(14,45)(15,46)(16,17)(18,37)(19,38)(21,32)(22,33)(24,29)(25,30)(26,57)(27,58)(28,56)(34,52)(35,54)(36,50)(39,55)(40,53)(41,51)(42,49)(43,47)(44,48);;
s3 := (12,13)(14,15)(16,26)(18,22)(19,21)(20,34)(23,39)(24,42)(25,27)(28,44)(29,30)(31,47)(32,50)(33,40)(35,38)(36,54)(37,51)(41,53)(45,56)(46,48)(49,58)(52,55);;
s4 := (11,19)(12,15)(13,30)(14,18)(16,33)(17,22)(20,25)(21,29)(23,46)(24,32)(26,36)(27,53)(28,39)(31,38)(34,49)(35,44)(37,45)(40,58)(41,47)(42,52)(43,51)(48,54)(50,57)(55,56);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s4*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s3, 
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(58)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(58)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(58)!(11,31)(12,23)(13,20)(14,45)(15,46)(16,17)(18,37)(19,38)(21,32)(22,33)(24,29)(25,30)(26,57)(27,58)(28,56)(34,52)(35,54)(36,50)(39,55)(40,53)(41,51)(42,49)(43,47)(44,48);
s3 := Sym(58)!(12,13)(14,15)(16,26)(18,22)(19,21)(20,34)(23,39)(24,42)(25,27)(28,44)(29,30)(31,47)(32,50)(33,40)(35,38)(36,54)(37,51)(41,53)(45,56)(46,48)(49,58)(52,55);
s4 := Sym(58)!(11,19)(12,15)(13,30)(14,18)(16,33)(17,22)(20,25)(21,29)(23,46)(24,32)(26,36)(27,53)(28,39)(31,38)(34,49)(35,44)(37,45)(40,58)(41,47)(42,52)(43,51)(48,54)(50,57)(55,56);
poly := sub<Sym(58)|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*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s4*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;