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Polytope of Type {15,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,30}*900
if this polytope has a name.
Group : SmallGroup(900,137)
Rank : 3
Schlafli Type : {15,30}
Number of vertices, edges, etc : 15, 225, 30
Order of s0s1s2 : 30
Order of s0s1s2s1 : 30
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {15,30,2} of size 1800
Vertex Figure Of :
   {2,15,30} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {15,10}*300
   5-fold quotients : {15,6}*180
   9-fold quotients : {5,10}*100
   15-fold quotients : {15,2}*60
   25-fold quotients : {3,6}*36
   45-fold quotients : {5,2}*20
   75-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {30,30}*1800i
Permutation Representation (GAP) :
s0 := (  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26, 51)( 27, 55)( 28, 54)( 29, 53)
( 30, 52)( 31, 71)( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 66)( 37, 70)
( 38, 69)( 39, 68)( 40, 67)( 41, 61)( 42, 65)( 43, 64)( 44, 63)( 45, 62)
( 46, 56)( 47, 60)( 48, 59)( 49, 58)( 50, 57)( 76,151)( 77,155)( 78,154)
( 79,153)( 80,152)( 81,171)( 82,175)( 83,174)( 84,173)( 85,172)( 86,166)
( 87,170)( 88,169)( 89,168)( 90,167)( 91,161)( 92,165)( 93,164)( 94,163)
( 95,162)( 96,156)( 97,160)( 98,159)( 99,158)(100,157)(101,201)(102,205)
(103,204)(104,203)(105,202)(106,221)(107,225)(108,224)(109,223)(110,222)
(111,216)(112,220)(113,219)(114,218)(115,217)(116,211)(117,215)(118,214)
(119,213)(120,212)(121,206)(122,210)(123,209)(124,208)(125,207)(126,176)
(127,180)(128,179)(129,178)(130,177)(131,196)(132,200)(133,199)(134,198)
(135,197)(136,191)(137,195)(138,194)(139,193)(140,192)(141,186)(142,190)
(143,189)(144,188)(145,187)(146,181)(147,185)(148,184)(149,183)(150,182);;
s1 := (  1,107)(  2,106)(  3,110)(  4,109)(  5,108)(  6,102)(  7,101)(  8,105)
(  9,104)( 10,103)( 11,122)( 12,121)( 13,125)( 14,124)( 15,123)( 16,117)
( 17,116)( 18,120)( 19,119)( 20,118)( 21,112)( 22,111)( 23,115)( 24,114)
( 25,113)( 26, 82)( 27, 81)( 28, 85)( 29, 84)( 30, 83)( 31, 77)( 32, 76)
( 33, 80)( 34, 79)( 35, 78)( 36, 97)( 37, 96)( 38,100)( 39, 99)( 40, 98)
( 41, 92)( 42, 91)( 43, 95)( 44, 94)( 45, 93)( 46, 87)( 47, 86)( 48, 90)
( 49, 89)( 50, 88)( 51,132)( 52,131)( 53,135)( 54,134)( 55,133)( 56,127)
( 57,126)( 58,130)( 59,129)( 60,128)( 61,147)( 62,146)( 63,150)( 64,149)
( 65,148)( 66,142)( 67,141)( 68,145)( 69,144)( 70,143)( 71,137)( 72,136)
( 73,140)( 74,139)( 75,138)(151,182)(152,181)(153,185)(154,184)(155,183)
(156,177)(157,176)(158,180)(159,179)(160,178)(161,197)(162,196)(163,200)
(164,199)(165,198)(166,192)(167,191)(168,195)(169,194)(170,193)(171,187)
(172,186)(173,190)(174,189)(175,188)(201,207)(202,206)(203,210)(204,209)
(205,208)(211,222)(212,221)(213,225)(214,224)(215,223)(216,217)(218,220);;
s2 := (  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)( 77, 80)( 78, 79)( 82, 85)( 83, 84)( 87, 90)
( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)(101,126)(102,130)(103,129)
(104,128)(105,127)(106,131)(107,135)(108,134)(109,133)(110,132)(111,136)
(112,140)(113,139)(114,138)(115,137)(116,141)(117,145)(118,144)(119,143)
(120,142)(121,146)(122,150)(123,149)(124,148)(125,147)(152,155)(153,154)
(157,160)(158,159)(162,165)(163,164)(167,170)(168,169)(172,175)(173,174)
(176,201)(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)(183,209)
(184,208)(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)(191,216)
(192,220)(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)(199,223)
(200,222);;
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*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(225)!(  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)
( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26, 51)( 27, 55)( 28, 54)
( 29, 53)( 30, 52)( 31, 71)( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 66)
( 37, 70)( 38, 69)( 39, 68)( 40, 67)( 41, 61)( 42, 65)( 43, 64)( 44, 63)
( 45, 62)( 46, 56)( 47, 60)( 48, 59)( 49, 58)( 50, 57)( 76,151)( 77,155)
( 78,154)( 79,153)( 80,152)( 81,171)( 82,175)( 83,174)( 84,173)( 85,172)
( 86,166)( 87,170)( 88,169)( 89,168)( 90,167)( 91,161)( 92,165)( 93,164)
( 94,163)( 95,162)( 96,156)( 97,160)( 98,159)( 99,158)(100,157)(101,201)
(102,205)(103,204)(104,203)(105,202)(106,221)(107,225)(108,224)(109,223)
(110,222)(111,216)(112,220)(113,219)(114,218)(115,217)(116,211)(117,215)
(118,214)(119,213)(120,212)(121,206)(122,210)(123,209)(124,208)(125,207)
(126,176)(127,180)(128,179)(129,178)(130,177)(131,196)(132,200)(133,199)
(134,198)(135,197)(136,191)(137,195)(138,194)(139,193)(140,192)(141,186)
(142,190)(143,189)(144,188)(145,187)(146,181)(147,185)(148,184)(149,183)
(150,182);
s1 := Sym(225)!(  1,107)(  2,106)(  3,110)(  4,109)(  5,108)(  6,102)(  7,101)
(  8,105)(  9,104)( 10,103)( 11,122)( 12,121)( 13,125)( 14,124)( 15,123)
( 16,117)( 17,116)( 18,120)( 19,119)( 20,118)( 21,112)( 22,111)( 23,115)
( 24,114)( 25,113)( 26, 82)( 27, 81)( 28, 85)( 29, 84)( 30, 83)( 31, 77)
( 32, 76)( 33, 80)( 34, 79)( 35, 78)( 36, 97)( 37, 96)( 38,100)( 39, 99)
( 40, 98)( 41, 92)( 42, 91)( 43, 95)( 44, 94)( 45, 93)( 46, 87)( 47, 86)
( 48, 90)( 49, 89)( 50, 88)( 51,132)( 52,131)( 53,135)( 54,134)( 55,133)
( 56,127)( 57,126)( 58,130)( 59,129)( 60,128)( 61,147)( 62,146)( 63,150)
( 64,149)( 65,148)( 66,142)( 67,141)( 68,145)( 69,144)( 70,143)( 71,137)
( 72,136)( 73,140)( 74,139)( 75,138)(151,182)(152,181)(153,185)(154,184)
(155,183)(156,177)(157,176)(158,180)(159,179)(160,178)(161,197)(162,196)
(163,200)(164,199)(165,198)(166,192)(167,191)(168,195)(169,194)(170,193)
(171,187)(172,186)(173,190)(174,189)(175,188)(201,207)(202,206)(203,210)
(204,209)(205,208)(211,222)(212,221)(213,225)(214,224)(215,223)(216,217)
(218,220);
s2 := Sym(225)!(  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)( 77, 80)( 78, 79)( 82, 85)( 83, 84)
( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)(101,126)(102,130)
(103,129)(104,128)(105,127)(106,131)(107,135)(108,134)(109,133)(110,132)
(111,136)(112,140)(113,139)(114,138)(115,137)(116,141)(117,145)(118,144)
(119,143)(120,142)(121,146)(122,150)(123,149)(124,148)(125,147)(152,155)
(153,154)(157,160)(158,159)(162,165)(163,164)(167,170)(168,169)(172,175)
(173,174)(176,201)(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)
(183,209)(184,208)(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)
(191,216)(192,220)(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)
(199,223)(200,222);
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope