Polytope of Type {30,3} with group SmallGroup(900,95)

Overview

Group: SmallGroup(900,95)
Rank: 3
Schläfli Type: {30,3}
Vertices, edges, …: 150, 225, 15
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 30
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

3-fold

{10,3}*300

25-fold

{6,3}*36

75-fold

{2,3}*12

Covers minimal covers in bold

2-fold

{30,6}*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*s0*s2*(s1*s0)^2*s2*s1> of order 5

3 facets

3 of {30}*60

30 vertex figures

30 of {3}*6

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

7 facets

5 of {6}*12
2 of {30}*60

30 vertex figures

30 of {3}*6

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

References

None.

to this polytope.