Polytope of Type {30,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,20}*1200b
Also Known As : {30,20|2}. if this polytope has another name.
Group : SmallGroup(1200,841)
Rank : 3
Schlafli Type : {30,20}
Number of vertices, edges, etc : 30, 300, 20
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 : {30,10}*600b
   3-fold quotients : {10,20}*400a
   5-fold quotients : {6,20}*240a, {30,4}*240a
   6-fold quotients : {10,10}*200a
   10-fold quotients : {6,10}*120, {30,2}*120
   15-fold quotients : {2,20}*80, {10,4}*80
   20-fold quotients : {15,2}*60
   25-fold quotients : {6,4}*48a
   30-fold quotients : {2,10}*40, {10,2}*40
   50-fold quotients : {6,2}*24
   60-fold quotients : {2,5}*20, {5,2}*20
   75-fold quotients : {2,4}*16
   100-fold quotients : {3,2}*12
   150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 26, 51)( 27, 52)( 28, 53)( 29, 54)( 30, 55)( 31, 71)
( 32, 72)( 33, 73)( 34, 74)( 35, 75)( 36, 66)( 37, 67)( 38, 68)( 39, 69)
( 40, 70)( 41, 61)( 42, 62)( 43, 63)( 44, 64)( 45, 65)( 46, 56)( 47, 57)
( 48, 58)( 49, 59)( 50, 60)( 81, 96)( 82, 97)( 83, 98)( 84, 99)( 85,100)
( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)(101,126)(102,127)(103,128)
(104,129)(105,130)(106,146)(107,147)(108,148)(109,149)(110,150)(111,141)
(112,142)(113,143)(114,144)(115,145)(116,136)(117,137)(118,138)(119,139)
(120,140)(121,131)(122,132)(123,133)(124,134)(125,135)(156,171)(157,172)
(158,173)(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)
(176,201)(177,202)(178,203)(179,204)(180,205)(181,221)(182,222)(183,223)
(184,224)(185,225)(186,216)(187,217)(188,218)(189,219)(190,220)(191,211)
(192,212)(193,213)(194,214)(195,215)(196,206)(197,207)(198,208)(199,209)
(200,210)(231,246)(232,247)(233,248)(234,249)(235,250)(236,241)(237,242)
(238,243)(239,244)(240,245)(251,276)(252,277)(253,278)(254,279)(255,280)
(256,296)(257,297)(258,298)(259,299)(260,300)(261,291)(262,292)(263,293)
(264,294)(265,295)(266,286)(267,287)(268,288)(269,289)(270,290)(271,281)
(272,282)(273,283)(274,284)(275,285);;
s1 := (  1, 31)(  2, 35)(  3, 34)(  4, 33)(  5, 32)(  6, 26)(  7, 30)(  8, 29)
(  9, 28)( 10, 27)( 11, 46)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 41)
( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 36)( 22, 40)( 23, 39)( 24, 38)
( 25, 37)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 71)( 62, 75)
( 63, 74)( 64, 73)( 65, 72)( 67, 70)( 68, 69)( 76,106)( 77,110)( 78,109)
( 79,108)( 80,107)( 81,101)( 82,105)( 83,104)( 84,103)( 85,102)( 86,121)
( 87,125)( 88,124)( 89,123)( 90,122)( 91,116)( 92,120)( 93,119)( 94,118)
( 95,117)( 96,111)( 97,115)( 98,114)( 99,113)(100,112)(126,131)(127,135)
(128,134)(129,133)(130,132)(136,146)(137,150)(138,149)(139,148)(140,147)
(142,145)(143,144)(151,256)(152,260)(153,259)(154,258)(155,257)(156,251)
(157,255)(158,254)(159,253)(160,252)(161,271)(162,275)(163,274)(164,273)
(165,272)(166,266)(167,270)(168,269)(169,268)(170,267)(171,261)(172,265)
(173,264)(174,263)(175,262)(176,231)(177,235)(178,234)(179,233)(180,232)
(181,226)(182,230)(183,229)(184,228)(185,227)(186,246)(187,250)(188,249)
(189,248)(190,247)(191,241)(192,245)(193,244)(194,243)(195,242)(196,236)
(197,240)(198,239)(199,238)(200,237)(201,281)(202,285)(203,284)(204,283)
(205,282)(206,276)(207,280)(208,279)(209,278)(210,277)(211,296)(212,300)
(213,299)(214,298)(215,297)(216,291)(217,295)(218,294)(219,293)(220,292)
(221,286)(222,290)(223,289)(224,288)(225,287);;
s2 := (  1,152)(  2,151)(  3,155)(  4,154)(  5,153)(  6,157)(  7,156)(  8,160)
(  9,159)( 10,158)( 11,162)( 12,161)( 13,165)( 14,164)( 15,163)( 16,167)
( 17,166)( 18,170)( 19,169)( 20,168)( 21,172)( 22,171)( 23,175)( 24,174)
( 25,173)( 26,177)( 27,176)( 28,180)( 29,179)( 30,178)( 31,182)( 32,181)
( 33,185)( 34,184)( 35,183)( 36,187)( 37,186)( 38,190)( 39,189)( 40,188)
( 41,192)( 42,191)( 43,195)( 44,194)( 45,193)( 46,197)( 47,196)( 48,200)
( 49,199)( 50,198)( 51,202)( 52,201)( 53,205)( 54,204)( 55,203)( 56,207)
( 57,206)( 58,210)( 59,209)( 60,208)( 61,212)( 62,211)( 63,215)( 64,214)
( 65,213)( 66,217)( 67,216)( 68,220)( 69,219)( 70,218)( 71,222)( 72,221)
( 73,225)( 74,224)( 75,223)( 76,227)( 77,226)( 78,230)( 79,229)( 80,228)
( 81,232)( 82,231)( 83,235)( 84,234)( 85,233)( 86,237)( 87,236)( 88,240)
( 89,239)( 90,238)( 91,242)( 92,241)( 93,245)( 94,244)( 95,243)( 96,247)
( 97,246)( 98,250)( 99,249)(100,248)(101,252)(102,251)(103,255)(104,254)
(105,253)(106,257)(107,256)(108,260)(109,259)(110,258)(111,262)(112,261)
(113,265)(114,264)(115,263)(116,267)(117,266)(118,270)(119,269)(120,268)
(121,272)(122,271)(123,275)(124,274)(125,273)(126,277)(127,276)(128,280)
(129,279)(130,278)(131,282)(132,281)(133,285)(134,284)(135,283)(136,287)
(137,286)(138,290)(139,289)(140,288)(141,292)(142,291)(143,295)(144,294)
(145,293)(146,297)(147,296)(148,300)(149,299)(150,298);;
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, 
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, 
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*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(300)!(  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 26, 51)( 27, 52)( 28, 53)( 29, 54)( 30, 55)
( 31, 71)( 32, 72)( 33, 73)( 34, 74)( 35, 75)( 36, 66)( 37, 67)( 38, 68)
( 39, 69)( 40, 70)( 41, 61)( 42, 62)( 43, 63)( 44, 64)( 45, 65)( 46, 56)
( 47, 57)( 48, 58)( 49, 59)( 50, 60)( 81, 96)( 82, 97)( 83, 98)( 84, 99)
( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)(101,126)(102,127)
(103,128)(104,129)(105,130)(106,146)(107,147)(108,148)(109,149)(110,150)
(111,141)(112,142)(113,143)(114,144)(115,145)(116,136)(117,137)(118,138)
(119,139)(120,140)(121,131)(122,132)(123,133)(124,134)(125,135)(156,171)
(157,172)(158,173)(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)
(165,170)(176,201)(177,202)(178,203)(179,204)(180,205)(181,221)(182,222)
(183,223)(184,224)(185,225)(186,216)(187,217)(188,218)(189,219)(190,220)
(191,211)(192,212)(193,213)(194,214)(195,215)(196,206)(197,207)(198,208)
(199,209)(200,210)(231,246)(232,247)(233,248)(234,249)(235,250)(236,241)
(237,242)(238,243)(239,244)(240,245)(251,276)(252,277)(253,278)(254,279)
(255,280)(256,296)(257,297)(258,298)(259,299)(260,300)(261,291)(262,292)
(263,293)(264,294)(265,295)(266,286)(267,287)(268,288)(269,289)(270,290)
(271,281)(272,282)(273,283)(274,284)(275,285);
s1 := Sym(300)!(  1, 31)(  2, 35)(  3, 34)(  4, 33)(  5, 32)(  6, 26)(  7, 30)
(  8, 29)(  9, 28)( 10, 27)( 11, 46)( 12, 50)( 13, 49)( 14, 48)( 15, 47)
( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 36)( 22, 40)( 23, 39)
( 24, 38)( 25, 37)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 71)
( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 67, 70)( 68, 69)( 76,106)( 77,110)
( 78,109)( 79,108)( 80,107)( 81,101)( 82,105)( 83,104)( 84,103)( 85,102)
( 86,121)( 87,125)( 88,124)( 89,123)( 90,122)( 91,116)( 92,120)( 93,119)
( 94,118)( 95,117)( 96,111)( 97,115)( 98,114)( 99,113)(100,112)(126,131)
(127,135)(128,134)(129,133)(130,132)(136,146)(137,150)(138,149)(139,148)
(140,147)(142,145)(143,144)(151,256)(152,260)(153,259)(154,258)(155,257)
(156,251)(157,255)(158,254)(159,253)(160,252)(161,271)(162,275)(163,274)
(164,273)(165,272)(166,266)(167,270)(168,269)(169,268)(170,267)(171,261)
(172,265)(173,264)(174,263)(175,262)(176,231)(177,235)(178,234)(179,233)
(180,232)(181,226)(182,230)(183,229)(184,228)(185,227)(186,246)(187,250)
(188,249)(189,248)(190,247)(191,241)(192,245)(193,244)(194,243)(195,242)
(196,236)(197,240)(198,239)(199,238)(200,237)(201,281)(202,285)(203,284)
(204,283)(205,282)(206,276)(207,280)(208,279)(209,278)(210,277)(211,296)
(212,300)(213,299)(214,298)(215,297)(216,291)(217,295)(218,294)(219,293)
(220,292)(221,286)(222,290)(223,289)(224,288)(225,287);
s2 := Sym(300)!(  1,152)(  2,151)(  3,155)(  4,154)(  5,153)(  6,157)(  7,156)
(  8,160)(  9,159)( 10,158)( 11,162)( 12,161)( 13,165)( 14,164)( 15,163)
( 16,167)( 17,166)( 18,170)( 19,169)( 20,168)( 21,172)( 22,171)( 23,175)
( 24,174)( 25,173)( 26,177)( 27,176)( 28,180)( 29,179)( 30,178)( 31,182)
( 32,181)( 33,185)( 34,184)( 35,183)( 36,187)( 37,186)( 38,190)( 39,189)
( 40,188)( 41,192)( 42,191)( 43,195)( 44,194)( 45,193)( 46,197)( 47,196)
( 48,200)( 49,199)( 50,198)( 51,202)( 52,201)( 53,205)( 54,204)( 55,203)
( 56,207)( 57,206)( 58,210)( 59,209)( 60,208)( 61,212)( 62,211)( 63,215)
( 64,214)( 65,213)( 66,217)( 67,216)( 68,220)( 69,219)( 70,218)( 71,222)
( 72,221)( 73,225)( 74,224)( 75,223)( 76,227)( 77,226)( 78,230)( 79,229)
( 80,228)( 81,232)( 82,231)( 83,235)( 84,234)( 85,233)( 86,237)( 87,236)
( 88,240)( 89,239)( 90,238)( 91,242)( 92,241)( 93,245)( 94,244)( 95,243)
( 96,247)( 97,246)( 98,250)( 99,249)(100,248)(101,252)(102,251)(103,255)
(104,254)(105,253)(106,257)(107,256)(108,260)(109,259)(110,258)(111,262)
(112,261)(113,265)(114,264)(115,263)(116,267)(117,266)(118,270)(119,269)
(120,268)(121,272)(122,271)(123,275)(124,274)(125,273)(126,277)(127,276)
(128,280)(129,279)(130,278)(131,282)(132,281)(133,285)(134,284)(135,283)
(136,287)(137,286)(138,290)(139,289)(140,288)(141,292)(142,291)(143,295)
(144,294)(145,293)(146,297)(147,296)(148,300)(149,299)(150,298);
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, 
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, 
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*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