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

Overview

Group: SmallGroup(900,95)
Rank: 3
Schläfli Type: {3,30}
Vertices, edges, …: 15, 225, 150
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

{3,10}*300

25-fold

{3,6}*36

75-fold

{3,2}*12

Covers minimal covers in bold

2-fold

{6,30}*1800d

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

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

30 facets

30 of {3}*6

3 vertex figures

3 of {30}*60

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

30 facets

30 of {3}*6

7 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.