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

Overview

Group: SmallGroup(1800,575)
Rank: 4
Schläfli Type: {6,6,3}
Vertices, edges, …: 6, 150, 75, 25
Order of s₀s₁s₂s₃: 30
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{6,6|2},{6,3}₁₀}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

3-fold

{2,6,3}*600

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=<s1*s2*s1*s3*(s2*s1)^2*s3*s2> of order 5

5 facets

5 of {6,6}*72a

6 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.