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# Polytope of Type {30,10}

Atlas Canonical Name : {30,10}*600a
if this polytope has a name.
Group : SmallGroup(600,174)
Rank : 3
Schlafli Type : {30,10}
Number of vertices, edges, etc : 30, 150, 10
Order of s0s1s2 : 30
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{30,10,2} of size 1200
Vertex Figure Of :
{2,30,10} of size 1200
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {10,10}*200b
5-fold quotients : {6,10}*120
6-fold quotients : {10,5}*100
15-fold quotients : {2,10}*40
25-fold quotients : {6,2}*24
30-fold quotients : {2,5}*20
50-fold quotients : {3,2}*12
75-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {30,20}*1200a, {60,10}*1200a
3-fold covers : {90,10}*1800a, {30,30}*1800b, {30,30}*1800d
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)
(26,51)(27,55)(28,54)(29,53)(30,52)(31,56)(32,60)(33,59)(34,58)(35,57)(36,61)
(37,65)(38,64)(39,63)(40,62)(41,66)(42,70)(43,69)(44,68)(45,67)(46,71)(47,75)
(48,74)(49,73)(50,72);;
s1 := ( 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);;
s2 := ( 1, 6)( 2,10)( 3, 9)( 4, 8)( 5, 7)(11,21)(12,25)(13,24)(14,23)(15,22)
(17,20)(18,19)(26,31)(27,35)(28,34)(29,33)(30,32)(36,46)(37,50)(38,49)(39,48)
(40,47)(42,45)(43,44)(51,56)(52,60)(53,59)(54,58)(55,57)(61,71)(62,75)(63,74)
(64,73)(65,72)(67,70)(68,69);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;

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

References : None.
to this polytope