Part of the Atlas of Small Regular Polytopes

Polytope of Type {30,4}

Atlas Canonical Name {30,4}*1200b

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Overview

Group
SmallGroup(1200,961)
Rank
3
Schläfli Type
{30,4}
Vertices, edges, …
150, 300, 20
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)^4*s1*s2*s1> of order 2

11 facets

75 vertex figures

P/N, where N=<(s0*s1)^5*s2*(s1*s0)^4*s1*s2> of order 2

10 facets

75 vertex figures

P/N, where N=<(s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1> of order 5

4 facets

30 vertex figures

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

4 facets

30 vertex figures

P/N, where N=<(s0*s1)^6> of order 5

12 facets

30 vertex figures

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

7 facets

15 vertex figures

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

References

None.

to this polytope.

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