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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,15,10}*1800
if this polytope has a name.
Group : SmallGroup(1800,678)
Rank : 5
Schlafli Type : {3,2,15,10}
Number of vertices, edges, etc : 3, 3, 15, 75, 10
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 : {3,2,5,10}*600
   5-fold quotients : {3,2,15,2}*360
   15-fold quotients : {3,2,5,2}*120
   25-fold quotients : {3,2,3,2}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 8)( 6, 7)( 9,24)(10,28)(11,27)(12,26)(13,25)(14,19)(15,23)(16,22)
(17,21)(18,20)(29,54)(30,58)(31,57)(32,56)(33,55)(34,74)(35,78)(36,77)(37,76)
(38,75)(39,69)(40,73)(41,72)(42,71)(43,70)(44,64)(45,68)(46,67)(47,66)(48,65)
(49,59)(50,63)(51,62)(52,61)(53,60);;
s3 := ( 4,35)( 5,34)( 6,38)( 7,37)( 8,36)( 9,30)(10,29)(11,33)(12,32)(13,31)
(14,50)(15,49)(16,53)(17,52)(18,51)(19,45)(20,44)(21,48)(22,47)(23,46)(24,40)
(25,39)(26,43)(27,42)(28,41)(54,60)(55,59)(56,63)(57,62)(58,61)(64,75)(65,74)
(66,78)(67,77)(68,76)(69,70)(71,73);;
s4 := ( 9,24)(10,25)(11,26)(12,27)(13,28)(14,19)(15,20)(16,21)(17,22)(18,23)
(34,49)(35,50)(36,51)(37,52)(38,53)(39,44)(40,45)(41,46)(42,47)(43,48)(59,74)
(60,75)(61,76)(62,77)(63,78)(64,69)(65,70)(66,71)(67,72)(68,73);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(78)!(2,3);
s1 := Sym(78)!(1,2);
s2 := Sym(78)!( 5, 8)( 6, 7)( 9,24)(10,28)(11,27)(12,26)(13,25)(14,19)(15,23)
(16,22)(17,21)(18,20)(29,54)(30,58)(31,57)(32,56)(33,55)(34,74)(35,78)(36,77)
(37,76)(38,75)(39,69)(40,73)(41,72)(42,71)(43,70)(44,64)(45,68)(46,67)(47,66)
(48,65)(49,59)(50,63)(51,62)(52,61)(53,60);
s3 := Sym(78)!( 4,35)( 5,34)( 6,38)( 7,37)( 8,36)( 9,30)(10,29)(11,33)(12,32)
(13,31)(14,50)(15,49)(16,53)(17,52)(18,51)(19,45)(20,44)(21,48)(22,47)(23,46)
(24,40)(25,39)(26,43)(27,42)(28,41)(54,60)(55,59)(56,63)(57,62)(58,61)(64,75)
(65,74)(66,78)(67,77)(68,76)(69,70)(71,73);
s4 := Sym(78)!( 9,24)(10,25)(11,26)(12,27)(13,28)(14,19)(15,20)(16,21)(17,22)
(18,23)(34,49)(35,50)(36,51)(37,52)(38,53)(39,44)(40,45)(41,46)(42,47)(43,48)
(59,74)(60,75)(61,76)(62,77)(63,78)(64,69)(65,70)(66,71)(67,72)(68,73);
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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope