Polytope of Type {10,15,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,15,2,3}*1800
if this polytope has a name.
Group : SmallGroup(1800,678)
Rank : 5
Schlafli Type : {10,15,2,3}
Number of vertices, edges, etc : 10, 75, 15, 3, 3
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {10,5,2,3}*600
   5-fold quotients : {2,15,2,3}*360
   15-fold quotients : {2,5,2,3}*120
   25-fold quotients : {2,3,2,3}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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);;
s3 := (77,78);;
s4 := (76,77);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4, 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*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(78)!( 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(78)!( 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(78)!( 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);
s3 := Sym(78)!(77,78);
s4 := Sym(78)!(76,77);
poly := sub<Sym(78)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
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*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 >;

to this polytope