Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,12}

Atlas Canonical Name {10,12}*600

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Overview

Group
SmallGroup(600,170)
Rank
3
Schläfli Type
{10,12}
Vertices, edges, …
25, 150, 30
Order of s0s1s2
12
Order of s0s1s2s1
10
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

3-fold

Covers minimal covers in bold

2-fold

3-fold

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

References

None.

to this polytope.

Twisty Puzzle