Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,4,6}

Atlas Canonical Name {10,4,6}*1200

Overview

Group
SmallGroup(1200,961)
Rank
4
Schläfli Type
{10,4,6}
Vertices, edges, …
25, 50, 30, 6
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.