Polytope of Type {30,6} with group SmallGroup(1800,575)

Overview

Group: SmallGroup(1800,575)
Rank: 3
Schläfli Type: {30,6}
Vertices, edges, …: 150, 450, 30
Order of s₀s₁s₂: 6
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

{10,6}*600b

6-fold

{10,3}*300

25-fold

{6,6}*72a

75-fold

150-fold

225-fold

{2,2}*8

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*(s2*s1)^2*s0*(s1*s2)^2> of order 5

14 facets

10 of {6}*12
4 of {30}*60

30 vertex figures

30 of {6}*12

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

6 facets

6 of {30}*60

30 vertex figures

30 of {6}*12

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

References

None.

to this polytope.