Polytope of Type {9,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,10}*900
if this polytope has a name.
Group : SmallGroup(900,48)
Rank : 3
Schlafli Type : {9,10}
Number of vertices, edges, etc : 45, 225, 50
Order of s₀s₁s₂ : 18
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {9,10,2} of size 1800
Vertex Figure Of :
   {2,9,10} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,10}*300
   25-fold quotients : {9,2}*36
   75-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {18,10}*1800b
Permutation Representation (GAP) :

s0 := (  2, 11)(  3, 21)(  4,  6)(  5, 16)(  7, 14)(  8, 24)( 10, 19)( 13, 22)
( 15, 17)( 18, 25)( 26, 51)( 27, 61)( 28, 71)( 29, 56)( 30, 66)( 31, 54)
( 32, 64)( 33, 74)( 34, 59)( 35, 69)( 36, 52)( 37, 62)( 38, 72)( 39, 57)
( 40, 67)( 41, 55)( 42, 65)( 43, 75)( 44, 60)( 45, 70)( 46, 53)( 47, 63)
( 48, 73)( 49, 58)( 50, 68)( 76,176)( 77,186)( 78,196)( 79,181)( 80,191)
( 81,179)( 82,189)( 83,199)( 84,184)( 85,194)( 86,177)( 87,187)( 88,197)
( 89,182)( 90,192)( 91,180)( 92,190)( 93,200)( 94,185)( 95,195)( 96,178)
( 97,188)( 98,198)( 99,183)(100,193)(101,151)(102,161)(103,171)(104,156)
(105,166)(106,154)(107,164)(108,174)(109,159)(110,169)(111,152)(112,162)
(113,172)(114,157)(115,167)(116,155)(117,165)(118,175)(119,160)(120,170)
(121,153)(122,163)(123,173)(124,158)(125,168)(126,201)(127,211)(128,221)
(129,206)(130,216)(131,204)(132,214)(133,224)(134,209)(135,219)(136,202)
(137,212)(138,222)(139,207)(140,217)(141,205)(142,215)(143,225)(144,210)
(145,220)(146,203)(147,213)(148,223)(149,208)(150,218);;
s1 := (  1, 76)(  2, 95)(  3, 84)(  4, 98)(  5, 87)(  6, 81)(  7,100)(  8, 89)
(  9, 78)( 10, 92)( 11, 86)( 12, 80)( 13, 94)( 14, 83)( 15, 97)( 16, 91)
( 17, 85)( 18, 99)( 19, 88)( 20, 77)( 21, 96)( 22, 90)( 23, 79)( 24, 93)
( 25, 82)( 26,126)( 27,145)( 28,134)( 29,148)( 30,137)( 31,131)( 32,150)
( 33,139)( 34,128)( 35,142)( 36,136)( 37,130)( 38,144)( 39,133)( 40,147)
( 41,141)( 42,135)( 43,149)( 44,138)( 45,127)( 46,146)( 47,140)( 48,129)
( 49,143)( 50,132)( 51,101)( 52,120)( 53,109)( 54,123)( 55,112)( 56,106)
( 57,125)( 58,114)( 59,103)( 60,117)( 61,111)( 62,105)( 63,119)( 64,108)
( 65,122)( 66,116)( 67,110)( 68,124)( 69,113)( 70,102)( 71,121)( 72,115)
( 73,104)( 74,118)( 75,107)(151,176)(152,195)(153,184)(154,198)(155,187)
(156,181)(157,200)(158,189)(159,178)(160,192)(161,186)(162,180)(163,194)
(164,183)(165,197)(166,191)(167,185)(168,199)(169,188)(170,177)(171,196)
(172,190)(173,179)(174,193)(175,182)(202,220)(203,209)(204,223)(205,212)
(207,225)(208,214)(210,217)(213,219)(215,222)(218,224);;
s2 := (  1, 12)(  2, 11)(  3, 15)(  4, 14)(  5, 13)(  6,  7)(  8, 10)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 37)( 27, 36)( 28, 40)( 29, 39)
( 30, 38)( 31, 32)( 33, 35)( 41, 47)( 42, 46)( 43, 50)( 44, 49)( 45, 48)
( 51, 62)( 52, 61)( 53, 65)( 54, 64)( 55, 63)( 56, 57)( 58, 60)( 66, 72)
( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 87)( 77, 86)( 78, 90)( 79, 89)
( 80, 88)( 81, 82)( 83, 85)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)
(101,112)(102,111)(103,115)(104,114)(105,113)(106,107)(108,110)(116,122)
(117,121)(118,125)(119,124)(120,123)(126,137)(127,136)(128,140)(129,139)
(130,138)(131,132)(133,135)(141,147)(142,146)(143,150)(144,149)(145,148)
(151,162)(152,161)(153,165)(154,164)(155,163)(156,157)(158,160)(166,172)
(167,171)(168,175)(169,174)(170,173)(176,187)(177,186)(178,190)(179,189)
(180,188)(181,182)(183,185)(191,197)(192,196)(193,200)(194,199)(195,198)
(201,212)(202,211)(203,215)(204,214)(205,213)(206,207)(208,210)(216,222)
(217,221)(218,225)(219,224)(220,223);;
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, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(225)!(  2, 11)(  3, 21)(  4,  6)(  5, 16)(  7, 14)(  8, 24)( 10, 19)
( 13, 22)( 15, 17)( 18, 25)( 26, 51)( 27, 61)( 28, 71)( 29, 56)( 30, 66)
( 31, 54)( 32, 64)( 33, 74)( 34, 59)( 35, 69)( 36, 52)( 37, 62)( 38, 72)
( 39, 57)( 40, 67)( 41, 55)( 42, 65)( 43, 75)( 44, 60)( 45, 70)( 46, 53)
( 47, 63)( 48, 73)( 49, 58)( 50, 68)( 76,176)( 77,186)( 78,196)( 79,181)
( 80,191)( 81,179)( 82,189)( 83,199)( 84,184)( 85,194)( 86,177)( 87,187)
( 88,197)( 89,182)( 90,192)( 91,180)( 92,190)( 93,200)( 94,185)( 95,195)
( 96,178)( 97,188)( 98,198)( 99,183)(100,193)(101,151)(102,161)(103,171)
(104,156)(105,166)(106,154)(107,164)(108,174)(109,159)(110,169)(111,152)
(112,162)(113,172)(114,157)(115,167)(116,155)(117,165)(118,175)(119,160)
(120,170)(121,153)(122,163)(123,173)(124,158)(125,168)(126,201)(127,211)
(128,221)(129,206)(130,216)(131,204)(132,214)(133,224)(134,209)(135,219)
(136,202)(137,212)(138,222)(139,207)(140,217)(141,205)(142,215)(143,225)
(144,210)(145,220)(146,203)(147,213)(148,223)(149,208)(150,218);
s1 := Sym(225)!(  1, 76)(  2, 95)(  3, 84)(  4, 98)(  5, 87)(  6, 81)(  7,100)
(  8, 89)(  9, 78)( 10, 92)( 11, 86)( 12, 80)( 13, 94)( 14, 83)( 15, 97)
( 16, 91)( 17, 85)( 18, 99)( 19, 88)( 20, 77)( 21, 96)( 22, 90)( 23, 79)
( 24, 93)( 25, 82)( 26,126)( 27,145)( 28,134)( 29,148)( 30,137)( 31,131)
( 32,150)( 33,139)( 34,128)( 35,142)( 36,136)( 37,130)( 38,144)( 39,133)
( 40,147)( 41,141)( 42,135)( 43,149)( 44,138)( 45,127)( 46,146)( 47,140)
( 48,129)( 49,143)( 50,132)( 51,101)( 52,120)( 53,109)( 54,123)( 55,112)
( 56,106)( 57,125)( 58,114)( 59,103)( 60,117)( 61,111)( 62,105)( 63,119)
( 64,108)( 65,122)( 66,116)( 67,110)( 68,124)( 69,113)( 70,102)( 71,121)
( 72,115)( 73,104)( 74,118)( 75,107)(151,176)(152,195)(153,184)(154,198)
(155,187)(156,181)(157,200)(158,189)(159,178)(160,192)(161,186)(162,180)
(163,194)(164,183)(165,197)(166,191)(167,185)(168,199)(169,188)(170,177)
(171,196)(172,190)(173,179)(174,193)(175,182)(202,220)(203,209)(204,223)
(205,212)(207,225)(208,214)(210,217)(213,219)(215,222)(218,224);
s2 := Sym(225)!(  1, 12)(  2, 11)(  3, 15)(  4, 14)(  5, 13)(  6,  7)(  8, 10)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 37)( 27, 36)( 28, 40)
( 29, 39)( 30, 38)( 31, 32)( 33, 35)( 41, 47)( 42, 46)( 43, 50)( 44, 49)
( 45, 48)( 51, 62)( 52, 61)( 53, 65)( 54, 64)( 55, 63)( 56, 57)( 58, 60)
( 66, 72)( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 87)( 77, 86)( 78, 90)
( 79, 89)( 80, 88)( 81, 82)( 83, 85)( 91, 97)( 92, 96)( 93,100)( 94, 99)
( 95, 98)(101,112)(102,111)(103,115)(104,114)(105,113)(106,107)(108,110)
(116,122)(117,121)(118,125)(119,124)(120,123)(126,137)(127,136)(128,140)
(129,139)(130,138)(131,132)(133,135)(141,147)(142,146)(143,150)(144,149)
(145,148)(151,162)(152,161)(153,165)(154,164)(155,163)(156,157)(158,160)
(166,172)(167,171)(168,175)(169,174)(170,173)(176,187)(177,186)(178,190)
(179,189)(180,188)(181,182)(183,185)(191,197)(192,196)(193,200)(194,199)
(195,198)(201,212)(202,211)(203,215)(204,214)(205,213)(206,207)(208,210)
(216,222)(217,221)(218,225)(219,224)(220,223);
poly := sub<Sym(225)|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, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*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 >;

References : None.
to this polytope