Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,30}

Atlas Canonical Name {4,30}*1200b

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Overview

Group
SmallGroup(1200,961)
Rank
3
Schläfli Type
{4,30}
Vertices, edges, …
20, 300, 150
Order of s0s1s2
12
Order of s0s1s2s1
10
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

3-fold

6-fold

25-fold

50-fold

75-fold

100-fold

150-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*(s2*s1)^3*s0*s1*s2*s1> of order 2

75 facets

10 vertex figures

P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*(s2*s1)^3*s0*s1*s2> of order 2

75 facets

11 vertex figures

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^4*s2> of order 5

30 facets

4 vertex figures

P/N, where N=<(s1*s2)^6> of order 5

30 facets

12 vertex figures

P/N, where N=<(s0*s1*s2*s1)^2> of order 5

30 facets

4 vertex figures

P/N, where N=<(s1*s2)^6, s0*(s1*s2)^4*s1*s0*s1*s2*s1> of order 10

15 facets

7 vertex figures

Representations

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

References

None.

to this polytope.

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