Polytope of Type {6,3} with group SmallGroup(900,95) - Atlas of Small Regular Polytopes

Overview

Group: SmallGroup(900,95)
Rank: 3
Schläfli Type: {6,3}
Vertices, edges, …: 150, 225, 75
Order of s₀s₁s₂: 30
Order of s₀s₁s₂s₁: 6
Also known as: {6,3}_(5,5). if this polytope has another name.

Special Properties

Toroidal
Locally Spherical
Orientable

Quotients maximal quotients in bold

3-fold

{6,3}*300

25-fold

{6,3}*36

75-fold

{2,3}*12

Covers minimal covers in bold

2-fold

{6,6}*1800c

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)^2> of order 3

27 facets

3 of {2}*4
24 of {6}*12

50 vertex figures

50 of {3}*6

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

15 facets

15 of {6}*12

30 vertex figures

30 of {3}*6

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

15 facets

15 of {6}*12

30 vertex figures

30 of {3}*6

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.