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Polytope of Type {20,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,30}*1200b
Also Known As : {20,30|2}. if this polytope has another name.
Group : SmallGroup(1200,841)
Rank : 3
Schlafli Type : {20,30}
Number of vertices, edges, etc : 20, 300, 30
Order of s0s1s2 : 60
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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) :
   2-fold quotients : {10,30}*600b
   3-fold quotients : {20,10}*400a
   5-fold quotients : {20,6}*240a, {4,30}*240a
   6-fold quotients : {10,10}*200a
   10-fold quotients : {10,6}*120, {2,30}*120
   15-fold quotients : {20,2}*80, {4,10}*80
   20-fold quotients : {2,15}*60
   25-fold quotients : {4,6}*48a
   30-fold quotients : {2,10}*40, {10,2}*40
   50-fold quotients : {2,6}*24
   60-fold quotients : {2,5}*20, {5,2}*20
   75-fold quotients : {4,2}*16
   100-fold quotients : {2,3}*12
   150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)
( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)
(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)(118,119)
(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)
(142,145)(143,144)(147,150)(148,149)(151,226)(152,230)(153,229)(154,228)
(155,227)(156,231)(157,235)(158,234)(159,233)(160,232)(161,236)(162,240)
(163,239)(164,238)(165,237)(166,241)(167,245)(168,244)(169,243)(170,242)
(171,246)(172,250)(173,249)(174,248)(175,247)(176,251)(177,255)(178,254)
(179,253)(180,252)(181,256)(182,260)(183,259)(184,258)(185,257)(186,261)
(187,265)(188,264)(189,263)(190,262)(191,266)(192,270)(193,269)(194,268)
(195,267)(196,271)(197,275)(198,274)(199,273)(200,272)(201,276)(202,280)
(203,279)(204,278)(205,277)(206,281)(207,285)(208,284)(209,283)(210,282)
(211,286)(212,290)(213,289)(214,288)(215,287)(216,291)(217,295)(218,294)
(219,293)(220,292)(221,296)(222,300)(223,299)(224,298)(225,297);;
s1 := (  1,152)(  2,151)(  3,155)(  4,154)(  5,153)(  6,172)(  7,171)(  8,175)
(  9,174)( 10,173)( 11,167)( 12,166)( 13,170)( 14,169)( 15,168)( 16,162)
( 17,161)( 18,165)( 19,164)( 20,163)( 21,157)( 22,156)( 23,160)( 24,159)
( 25,158)( 26,202)( 27,201)( 28,205)( 29,204)( 30,203)( 31,222)( 32,221)
( 33,225)( 34,224)( 35,223)( 36,217)( 37,216)( 38,220)( 39,219)( 40,218)
( 41,212)( 42,211)( 43,215)( 44,214)( 45,213)( 46,207)( 47,206)( 48,210)
( 49,209)( 50,208)( 51,177)( 52,176)( 53,180)( 54,179)( 55,178)( 56,197)
( 57,196)( 58,200)( 59,199)( 60,198)( 61,192)( 62,191)( 63,195)( 64,194)
( 65,193)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,182)( 72,181)
( 73,185)( 74,184)( 75,183)( 76,227)( 77,226)( 78,230)( 79,229)( 80,228)
( 81,247)( 82,246)( 83,250)( 84,249)( 85,248)( 86,242)( 87,241)( 88,245)
( 89,244)( 90,243)( 91,237)( 92,236)( 93,240)( 94,239)( 95,238)( 96,232)
( 97,231)( 98,235)( 99,234)(100,233)(101,277)(102,276)(103,280)(104,279)
(105,278)(106,297)(107,296)(108,300)(109,299)(110,298)(111,292)(112,291)
(113,295)(114,294)(115,293)(116,287)(117,286)(118,290)(119,289)(120,288)
(121,282)(122,281)(123,285)(124,284)(125,283)(126,252)(127,251)(128,255)
(129,254)(130,253)(131,272)(132,271)(133,275)(134,274)(135,273)(136,267)
(137,266)(138,270)(139,269)(140,268)(141,262)(142,261)(143,265)(144,264)
(145,263)(146,257)(147,256)(148,260)(149,259)(150,258);;
s2 := (  1, 31)(  2, 32)(  3, 33)(  4, 34)(  5, 35)(  6, 26)(  7, 27)(  8, 28)
(  9, 29)( 10, 30)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 50)( 16, 41)
( 17, 42)( 18, 43)( 19, 44)( 20, 45)( 21, 36)( 22, 37)( 23, 38)( 24, 39)
( 25, 40)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61, 71)( 62, 72)
( 63, 73)( 64, 74)( 65, 75)( 76,106)( 77,107)( 78,108)( 79,109)( 80,110)
( 81,101)( 82,102)( 83,103)( 84,104)( 85,105)( 86,121)( 87,122)( 88,123)
( 89,124)( 90,125)( 91,116)( 92,117)( 93,118)( 94,119)( 95,120)( 96,111)
( 97,112)( 98,113)( 99,114)(100,115)(126,131)(127,132)(128,133)(129,134)
(130,135)(136,146)(137,147)(138,148)(139,149)(140,150)(151,181)(152,182)
(153,183)(154,184)(155,185)(156,176)(157,177)(158,178)(159,179)(160,180)
(161,196)(162,197)(163,198)(164,199)(165,200)(166,191)(167,192)(168,193)
(169,194)(170,195)(171,186)(172,187)(173,188)(174,189)(175,190)(201,206)
(202,207)(203,208)(204,209)(205,210)(211,221)(212,222)(213,223)(214,224)
(215,225)(226,256)(227,257)(228,258)(229,259)(230,260)(231,251)(232,252)
(233,253)(234,254)(235,255)(236,271)(237,272)(238,273)(239,274)(240,275)
(241,266)(242,267)(243,268)(244,269)(245,270)(246,261)(247,262)(248,263)
(249,264)(250,265)(276,281)(277,282)(278,283)(279,284)(280,285)(286,296)
(287,297)(288,298)(289,299)(290,300);;
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*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*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*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(300)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)
( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)
( 98, 99)(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)
(118,119)(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)
(138,139)(142,145)(143,144)(147,150)(148,149)(151,226)(152,230)(153,229)
(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)(160,232)(161,236)
(162,240)(163,239)(164,238)(165,237)(166,241)(167,245)(168,244)(169,243)
(170,242)(171,246)(172,250)(173,249)(174,248)(175,247)(176,251)(177,255)
(178,254)(179,253)(180,252)(181,256)(182,260)(183,259)(184,258)(185,257)
(186,261)(187,265)(188,264)(189,263)(190,262)(191,266)(192,270)(193,269)
(194,268)(195,267)(196,271)(197,275)(198,274)(199,273)(200,272)(201,276)
(202,280)(203,279)(204,278)(205,277)(206,281)(207,285)(208,284)(209,283)
(210,282)(211,286)(212,290)(213,289)(214,288)(215,287)(216,291)(217,295)
(218,294)(219,293)(220,292)(221,296)(222,300)(223,299)(224,298)(225,297);
s1 := Sym(300)!(  1,152)(  2,151)(  3,155)(  4,154)(  5,153)(  6,172)(  7,171)
(  8,175)(  9,174)( 10,173)( 11,167)( 12,166)( 13,170)( 14,169)( 15,168)
( 16,162)( 17,161)( 18,165)( 19,164)( 20,163)( 21,157)( 22,156)( 23,160)
( 24,159)( 25,158)( 26,202)( 27,201)( 28,205)( 29,204)( 30,203)( 31,222)
( 32,221)( 33,225)( 34,224)( 35,223)( 36,217)( 37,216)( 38,220)( 39,219)
( 40,218)( 41,212)( 42,211)( 43,215)( 44,214)( 45,213)( 46,207)( 47,206)
( 48,210)( 49,209)( 50,208)( 51,177)( 52,176)( 53,180)( 54,179)( 55,178)
( 56,197)( 57,196)( 58,200)( 59,199)( 60,198)( 61,192)( 62,191)( 63,195)
( 64,194)( 65,193)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,182)
( 72,181)( 73,185)( 74,184)( 75,183)( 76,227)( 77,226)( 78,230)( 79,229)
( 80,228)( 81,247)( 82,246)( 83,250)( 84,249)( 85,248)( 86,242)( 87,241)
( 88,245)( 89,244)( 90,243)( 91,237)( 92,236)( 93,240)( 94,239)( 95,238)
( 96,232)( 97,231)( 98,235)( 99,234)(100,233)(101,277)(102,276)(103,280)
(104,279)(105,278)(106,297)(107,296)(108,300)(109,299)(110,298)(111,292)
(112,291)(113,295)(114,294)(115,293)(116,287)(117,286)(118,290)(119,289)
(120,288)(121,282)(122,281)(123,285)(124,284)(125,283)(126,252)(127,251)
(128,255)(129,254)(130,253)(131,272)(132,271)(133,275)(134,274)(135,273)
(136,267)(137,266)(138,270)(139,269)(140,268)(141,262)(142,261)(143,265)
(144,264)(145,263)(146,257)(147,256)(148,260)(149,259)(150,258);
s2 := Sym(300)!(  1, 31)(  2, 32)(  3, 33)(  4, 34)(  5, 35)(  6, 26)(  7, 27)
(  8, 28)(  9, 29)( 10, 30)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 50)
( 16, 41)( 17, 42)( 18, 43)( 19, 44)( 20, 45)( 21, 36)( 22, 37)( 23, 38)
( 24, 39)( 25, 40)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61, 71)
( 62, 72)( 63, 73)( 64, 74)( 65, 75)( 76,106)( 77,107)( 78,108)( 79,109)
( 80,110)( 81,101)( 82,102)( 83,103)( 84,104)( 85,105)( 86,121)( 87,122)
( 88,123)( 89,124)( 90,125)( 91,116)( 92,117)( 93,118)( 94,119)( 95,120)
( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(126,131)(127,132)(128,133)
(129,134)(130,135)(136,146)(137,147)(138,148)(139,149)(140,150)(151,181)
(152,182)(153,183)(154,184)(155,185)(156,176)(157,177)(158,178)(159,179)
(160,180)(161,196)(162,197)(163,198)(164,199)(165,200)(166,191)(167,192)
(168,193)(169,194)(170,195)(171,186)(172,187)(173,188)(174,189)(175,190)
(201,206)(202,207)(203,208)(204,209)(205,210)(211,221)(212,222)(213,223)
(214,224)(215,225)(226,256)(227,257)(228,258)(229,259)(230,260)(231,251)
(232,252)(233,253)(234,254)(235,255)(236,271)(237,272)(238,273)(239,274)
(240,275)(241,266)(242,267)(243,268)(244,269)(245,270)(246,261)(247,262)
(248,263)(249,264)(250,265)(276,281)(277,282)(278,283)(279,284)(280,285)
(286,296)(287,297)(288,298)(289,299)(290,300);
poly := sub<Sym(300)|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*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*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*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 >; 
 
References : None.
to this polytope