Polytope of Type {10,15} with group SmallGroup(300,39)

Overview

Group: SmallGroup(300,39)
Rank: 3
Schläfli Type: {10,15}
Vertices, edges, …: 10, 75, 15
Order of s₀s₁s₂: 30
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

3-fold

{10,5}*100

5-fold

{2,15}*60

15-fold

{2,5}*20

25-fold

{2,3}*12

Covers minimal covers in bold

2-fold

{10,30}*600c

3-fold

4-fold

5-fold

6-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References