Polytope of Type {10,3,6} with group SmallGroup(1800,575)

Overview

Group: SmallGroup(1800,575)
Rank: 4
Schläfli Type: {10,3,6}
Vertices, edges, …: 50, 75, 45, 6
Order of s₀s₁s₂s₃: 6
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

3-fold

{10,3,2}*600

25-fold

{2,3,6}*72

75-fold

{2,3,2}*24

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*s1)^2> of order 5

6 facets

6 of 5-fold non-regular quotient of {10,3}*300

10 vertex figures

10 of {3,6}*36

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

6 facets

6 of 5-fold non-regular quotient of {10,3}*300

10 vertex figures

10 of {3,6}*36

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)(27,30)(28,29)(31,46)(32,50)(33,49)(34,48)(35,47)(36,41)(37,45)(38,44)(39,43)(40,42)(52,55)(53,54)(56,71)(57,75)(58,74)(59,73)(60,72)(61,66)(62,70)(63,69)(64,68)(65,67);;
s1 := ( 1, 2)( 3, 5)( 6, 8)( 9,10)(11,14)(12,13)(16,20)(17,19)(22,25)(23,24)(26,52)(27,51)(28,55)(29,54)(30,53)(31,58)(32,57)(33,56)(34,60)(35,59)(36,64)(37,63)(38,62)(39,61)(40,65)(41,70)(42,69)(43,68)(44,67)(45,66)(46,71)(47,75)(48,74)(49,73)(50,72);;
s2 := ( 1,26)( 2,32)( 3,38)( 4,44)( 5,50)( 6,46)( 7,27)( 8,33)( 9,39)(10,45)(11,41)(12,47)(13,28)(14,34)(15,40)(16,36)(17,42)(18,48)(19,29)(20,35)(21,31)(22,37)(23,43)(24,49)(25,30)(52,57)(53,63)(54,69)(55,75)(56,71)(59,64)(60,70)(61,66)(62,72)(68,73);;
s3 := (26,51)(27,52)(28,53)(29,54)(30,55)(31,56)(32,57)(33,58)(34,59)(35,60)(36,61)(37,62)(38,63)(39,64)(40,65)(41,66)(42,67)(43,68)(44,69)(45,70)(46,71)(47,72)(48,73)(49,74)(50,75);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*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*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)(27,30)(28,29)(31,46)(32,50)(33,49)(34,48)(35,47)(36,41)(37,45)(38,44)(39,43)(40,42)(52,55)(53,54)(56,71)(57,75)(58,74)(59,73)(60,72)(61,66)(62,70)(63,69)(64,68)(65,67);
s1 := Sym(75)!( 1, 2)( 3, 5)( 6, 8)( 9,10)(11,14)(12,13)(16,20)(17,19)(22,25)(23,24)(26,52)(27,51)(28,55)(29,54)(30,53)(31,58)(32,57)(33,56)(34,60)(35,59)(36,64)(37,63)(38,62)(39,61)(40,65)(41,70)(42,69)(43,68)(44,67)(45,66)(46,71)(47,75)(48,74)(49,73)(50,72);
s2 := Sym(75)!( 1,26)( 2,32)( 3,38)( 4,44)( 5,50)( 6,46)( 7,27)( 8,33)( 9,39)(10,45)(11,41)(12,47)(13,28)(14,34)(15,40)(16,36)(17,42)(18,48)(19,29)(20,35)(21,31)(22,37)(23,43)(24,49)(25,30)(52,57)(53,63)(54,69)(55,75)(56,71)(59,64)(60,70)(61,66)(62,72)(68,73);
s3 := Sym(75)!(26,51)(27,52)(28,53)(29,54)(30,55)(31,56)(32,57)(33,58)(34,59)(35,60)(36,61)(37,62)(38,63)(39,64)(40,65)(41,66)(42,67)(43,68)(44,69)(45,70)(46,71)(47,72)(48,73)(49,74)(50,75);
poly := sub<Sym(75)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*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*s0*s1 >;

References

None.

to this polytope.