Polytope of Type {50,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {50,12}*1200
Also Known As : {50,12|2}. if this polytope has another name.
Group : SmallGroup(1200,130)
Rank : 3
Schlafli Type : {50,12}
Number of vertices, edges, etc : 50, 300, 12
Order of s₀s₁s₂ : 300
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 : {50,6}*600
   3-fold quotients : {50,4}*400
   5-fold quotients : {10,12}*240
   6-fold quotients : {50,2}*200
   10-fold quotients : {10,6}*120
   12-fold quotients : {25,2}*100
   15-fold quotients : {10,4}*80
   25-fold quotients : {2,12}*48
   30-fold quotients : {10,2}*40
   50-fold quotients : {2,6}*24
   60-fold quotients : {5,2}*20
   75-fold quotients : {2,4}*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)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)( 11, 20)
( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)( 32, 49)
( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)
( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)( 61, 70)
( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 77, 80)( 78, 79)( 81,100)( 82, 99)
( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)( 90, 91)
(102,105)(103,104)(106,125)(107,124)(108,123)(109,122)(110,121)(111,120)
(112,119)(113,118)(114,117)(115,116)(127,130)(128,129)(131,150)(132,149)
(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)(140,141)
(152,155)(153,154)(156,175)(157,174)(158,173)(159,172)(160,171)(161,170)
(162,169)(163,168)(164,167)(165,166)(177,180)(178,179)(181,200)(182,199)
(183,198)(184,197)(185,196)(186,195)(187,194)(188,193)(189,192)(190,191)
(202,205)(203,204)(206,225)(207,224)(208,223)(209,222)(210,221)(211,220)
(212,219)(213,218)(214,217)(215,216)(227,230)(228,229)(231,250)(232,249)
(233,248)(234,247)(235,246)(236,245)(237,244)(238,243)(239,242)(240,241)
(252,255)(253,254)(256,275)(257,274)(258,273)(259,272)(260,271)(261,270)
(262,269)(263,268)(264,267)(265,266)(277,280)(278,279)(281,300)(282,299)
(283,298)(284,297)(285,296)(286,295)(287,294)(288,293)(289,292)(290,291);;
s1 := (  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 25)( 12, 24)( 13, 23)
( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 26, 56)( 27, 60)( 28, 59)( 29, 58)
( 30, 57)( 31, 51)( 32, 55)( 33, 54)( 34, 53)( 35, 52)( 36, 75)( 37, 74)
( 38, 73)( 39, 72)( 40, 71)( 41, 70)( 42, 69)( 43, 68)( 44, 67)( 45, 66)
( 46, 65)( 47, 64)( 48, 63)( 49, 62)( 50, 61)( 76, 81)( 77, 85)( 78, 84)
( 79, 83)( 80, 82)( 86,100)( 87, 99)( 88, 98)( 89, 97)( 90, 96)( 91, 95)
( 92, 94)(101,131)(102,135)(103,134)(104,133)(105,132)(106,126)(107,130)
(108,129)(109,128)(110,127)(111,150)(112,149)(113,148)(114,147)(115,146)
(116,145)(117,144)(118,143)(119,142)(120,141)(121,140)(122,139)(123,138)
(124,137)(125,136)(151,231)(152,235)(153,234)(154,233)(155,232)(156,226)
(157,230)(158,229)(159,228)(160,227)(161,250)(162,249)(163,248)(164,247)
(165,246)(166,245)(167,244)(168,243)(169,242)(170,241)(171,240)(172,239)
(173,238)(174,237)(175,236)(176,281)(177,285)(178,284)(179,283)(180,282)
(181,276)(182,280)(183,279)(184,278)(185,277)(186,300)(187,299)(188,298)
(189,297)(190,296)(191,295)(192,294)(193,293)(194,292)(195,291)(196,290)
(197,289)(198,288)(199,287)(200,286)(201,256)(202,260)(203,259)(204,258)
(205,257)(206,251)(207,255)(208,254)(209,253)(210,252)(211,275)(212,274)
(213,273)(214,272)(215,271)(216,270)(217,269)(218,268)(219,267)(220,266)
(221,265)(222,264)(223,263)(224,262)(225,261);;
s2 := (  1,176)(  2,177)(  3,178)(  4,179)(  5,180)(  6,181)(  7,182)(  8,183)
(  9,184)( 10,185)( 11,186)( 12,187)( 13,188)( 14,189)( 15,190)( 16,191)
( 17,192)( 18,193)( 19,194)( 20,195)( 21,196)( 22,197)( 23,198)( 24,199)
( 25,200)( 26,151)( 27,152)( 28,153)( 29,154)( 30,155)( 31,156)( 32,157)
( 33,158)( 34,159)( 35,160)( 36,161)( 37,162)( 38,163)( 39,164)( 40,165)
( 41,166)( 42,167)( 43,168)( 44,169)( 45,170)( 46,171)( 47,172)( 48,173)
( 49,174)( 50,175)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)( 56,206)
( 57,207)( 58,208)( 59,209)( 60,210)( 61,211)( 62,212)( 63,213)( 64,214)
( 65,215)( 66,216)( 67,217)( 68,218)( 69,219)( 70,220)( 71,221)( 72,222)
( 73,223)( 74,224)( 75,225)( 76,251)( 77,252)( 78,253)( 79,254)( 80,255)
( 81,256)( 82,257)( 83,258)( 84,259)( 85,260)( 86,261)( 87,262)( 88,263)
( 89,264)( 90,265)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)( 96,271)
( 97,272)( 98,273)( 99,274)(100,275)(101,226)(102,227)(103,228)(104,229)
(105,230)(106,231)(107,232)(108,233)(109,234)(110,235)(111,236)(112,237)
(113,238)(114,239)(115,240)(116,241)(117,242)(118,243)(119,244)(120,245)
(121,246)(122,247)(123,248)(124,249)(125,250)(126,276)(127,277)(128,278)
(129,279)(130,280)(131,281)(132,282)(133,283)(134,284)(135,285)(136,286)
(137,287)(138,288)(139,289)(140,290)(141,291)(142,292)(143,293)(144,294)
(145,295)(146,296)(147,297)(148,298)(149,299)(150,300);;
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, 
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*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)!(  2,  5)(  3,  4)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)
( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)
( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)
( 40, 41)( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)
( 61, 70)( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 77, 80)( 78, 79)( 81,100)
( 82, 99)( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)
( 90, 91)(102,105)(103,104)(106,125)(107,124)(108,123)(109,122)(110,121)
(111,120)(112,119)(113,118)(114,117)(115,116)(127,130)(128,129)(131,150)
(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)
(140,141)(152,155)(153,154)(156,175)(157,174)(158,173)(159,172)(160,171)
(161,170)(162,169)(163,168)(164,167)(165,166)(177,180)(178,179)(181,200)
(182,199)(183,198)(184,197)(185,196)(186,195)(187,194)(188,193)(189,192)
(190,191)(202,205)(203,204)(206,225)(207,224)(208,223)(209,222)(210,221)
(211,220)(212,219)(213,218)(214,217)(215,216)(227,230)(228,229)(231,250)
(232,249)(233,248)(234,247)(235,246)(236,245)(237,244)(238,243)(239,242)
(240,241)(252,255)(253,254)(256,275)(257,274)(258,273)(259,272)(260,271)
(261,270)(262,269)(263,268)(264,267)(265,266)(277,280)(278,279)(281,300)
(282,299)(283,298)(284,297)(285,296)(286,295)(287,294)(288,293)(289,292)
(290,291);
s1 := Sym(300)!(  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 25)( 12, 24)
( 13, 23)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 26, 56)( 27, 60)( 28, 59)
( 29, 58)( 30, 57)( 31, 51)( 32, 55)( 33, 54)( 34, 53)( 35, 52)( 36, 75)
( 37, 74)( 38, 73)( 39, 72)( 40, 71)( 41, 70)( 42, 69)( 43, 68)( 44, 67)
( 45, 66)( 46, 65)( 47, 64)( 48, 63)( 49, 62)( 50, 61)( 76, 81)( 77, 85)
( 78, 84)( 79, 83)( 80, 82)( 86,100)( 87, 99)( 88, 98)( 89, 97)( 90, 96)
( 91, 95)( 92, 94)(101,131)(102,135)(103,134)(104,133)(105,132)(106,126)
(107,130)(108,129)(109,128)(110,127)(111,150)(112,149)(113,148)(114,147)
(115,146)(116,145)(117,144)(118,143)(119,142)(120,141)(121,140)(122,139)
(123,138)(124,137)(125,136)(151,231)(152,235)(153,234)(154,233)(155,232)
(156,226)(157,230)(158,229)(159,228)(160,227)(161,250)(162,249)(163,248)
(164,247)(165,246)(166,245)(167,244)(168,243)(169,242)(170,241)(171,240)
(172,239)(173,238)(174,237)(175,236)(176,281)(177,285)(178,284)(179,283)
(180,282)(181,276)(182,280)(183,279)(184,278)(185,277)(186,300)(187,299)
(188,298)(189,297)(190,296)(191,295)(192,294)(193,293)(194,292)(195,291)
(196,290)(197,289)(198,288)(199,287)(200,286)(201,256)(202,260)(203,259)
(204,258)(205,257)(206,251)(207,255)(208,254)(209,253)(210,252)(211,275)
(212,274)(213,273)(214,272)(215,271)(216,270)(217,269)(218,268)(219,267)
(220,266)(221,265)(222,264)(223,263)(224,262)(225,261);
s2 := Sym(300)!(  1,176)(  2,177)(  3,178)(  4,179)(  5,180)(  6,181)(  7,182)
(  8,183)(  9,184)( 10,185)( 11,186)( 12,187)( 13,188)( 14,189)( 15,190)
( 16,191)( 17,192)( 18,193)( 19,194)( 20,195)( 21,196)( 22,197)( 23,198)
( 24,199)( 25,200)( 26,151)( 27,152)( 28,153)( 29,154)( 30,155)( 31,156)
( 32,157)( 33,158)( 34,159)( 35,160)( 36,161)( 37,162)( 38,163)( 39,164)
( 40,165)( 41,166)( 42,167)( 43,168)( 44,169)( 45,170)( 46,171)( 47,172)
( 48,173)( 49,174)( 50,175)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)
( 56,206)( 57,207)( 58,208)( 59,209)( 60,210)( 61,211)( 62,212)( 63,213)
( 64,214)( 65,215)( 66,216)( 67,217)( 68,218)( 69,219)( 70,220)( 71,221)
( 72,222)( 73,223)( 74,224)( 75,225)( 76,251)( 77,252)( 78,253)( 79,254)
( 80,255)( 81,256)( 82,257)( 83,258)( 84,259)( 85,260)( 86,261)( 87,262)
( 88,263)( 89,264)( 90,265)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)
( 96,271)( 97,272)( 98,273)( 99,274)(100,275)(101,226)(102,227)(103,228)
(104,229)(105,230)(106,231)(107,232)(108,233)(109,234)(110,235)(111,236)
(112,237)(113,238)(114,239)(115,240)(116,241)(117,242)(118,243)(119,244)
(120,245)(121,246)(122,247)(123,248)(124,249)(125,250)(126,276)(127,277)
(128,278)(129,279)(130,280)(131,281)(132,282)(133,283)(134,284)(135,285)
(136,286)(137,287)(138,288)(139,289)(140,290)(141,291)(142,292)(143,293)
(144,294)(145,295)(146,296)(147,297)(148,298)(149,299)(150,300);
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, 
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*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