Polytope of Type {4,150}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,150}*1200a
Also Known As : {4,150|2}. if this polytope has another name.
Group : SmallGroup(1200,173)
Rank : 3
Schlafli Type : {4,150}
Number of vertices, edges, etc : 4, 300, 150
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 : {2,150}*600
   3-fold quotients : {4,50}*400
   4-fold quotients : {2,75}*300
   5-fold quotients : {4,30}*240a
   6-fold quotients : {2,50}*200
   10-fold quotients : {2,30}*120
   12-fold quotients : {2,25}*100
   15-fold quotients : {4,10}*80
   20-fold quotients : {2,15}*60
   25-fold quotients : {4,6}*48a
   30-fold quotients : {2,10}*40
   50-fold quotients : {2,6}*24
   60-fold quotients : {2,5}*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 := (151,226)(152,227)(153,228)(154,229)(155,230)(156,231)(157,232)(158,233)
(159,234)(160,235)(161,236)(162,237)(163,238)(164,239)(165,240)(166,241)
(167,242)(168,243)(169,244)(170,245)(171,246)(172,247)(173,248)(174,249)
(175,250)(176,251)(177,252)(178,253)(179,254)(180,255)(181,256)(182,257)
(183,258)(184,259)(185,260)(186,261)(187,262)(188,263)(189,264)(190,265)
(191,266)(192,267)(193,268)(194,269)(195,270)(196,271)(197,272)(198,273)
(199,274)(200,275)(201,276)(202,277)(203,278)(204,279)(205,280)(206,281)
(207,282)(208,283)(209,284)(210,285)(211,286)(212,287)(213,288)(214,289)
(215,290)(216,291)(217,292)(218,293)(219,294)(220,295)(221,296)(222,297)
(223,298)(224,299)(225,300);;
s1 := (  1,151)(  2,155)(  3,154)(  4,153)(  5,152)(  6,175)(  7,174)(  8,173)
(  9,172)( 10,171)( 11,170)( 12,169)( 13,168)( 14,167)( 15,166)( 16,165)
( 17,164)( 18,163)( 19,162)( 20,161)( 21,160)( 22,159)( 23,158)( 24,157)
( 25,156)( 26,201)( 27,205)( 28,204)( 29,203)( 30,202)( 31,225)( 32,224)
( 33,223)( 34,222)( 35,221)( 36,220)( 37,219)( 38,218)( 39,217)( 40,216)
( 41,215)( 42,214)( 43,213)( 44,212)( 45,211)( 46,210)( 47,209)( 48,208)
( 49,207)( 50,206)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)( 56,200)
( 57,199)( 58,198)( 59,197)( 60,196)( 61,195)( 62,194)( 63,193)( 64,192)
( 65,191)( 66,190)( 67,189)( 68,188)( 69,187)( 70,186)( 71,185)( 72,184)
( 73,183)( 74,182)( 75,181)( 76,226)( 77,230)( 78,229)( 79,228)( 80,227)
( 81,250)( 82,249)( 83,248)( 84,247)( 85,246)( 86,245)( 87,244)( 88,243)
( 89,242)( 90,241)( 91,240)( 92,239)( 93,238)( 94,237)( 95,236)( 96,235)
( 97,234)( 98,233)( 99,232)(100,231)(101,276)(102,280)(103,279)(104,278)
(105,277)(106,300)(107,299)(108,298)(109,297)(110,296)(111,295)(112,294)
(113,293)(114,292)(115,291)(116,290)(117,289)(118,288)(119,287)(120,286)
(121,285)(122,284)(123,283)(124,282)(125,281)(126,251)(127,255)(128,254)
(129,253)(130,252)(131,275)(132,274)(133,273)(134,272)(135,271)(136,270)
(137,269)(138,268)(139,267)(140,266)(141,265)(142,264)(143,263)(144,262)
(145,261)(146,260)(147,259)(148,258)(149,257)(150,256);;
s2 := (  1, 31)(  2, 35)(  3, 34)(  4, 33)(  5, 32)(  6, 26)(  7, 30)(  8, 29)
(  9, 28)( 10, 27)( 11, 50)( 12, 49)( 13, 48)( 14, 47)( 15, 46)( 16, 45)
( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 38)( 24, 37)
( 25, 36)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 75)( 62, 74)
( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 76,106)( 77,110)( 78,109)
( 79,108)( 80,107)( 81,101)( 82,105)( 83,104)( 84,103)( 85,102)( 86,125)
( 87,124)( 88,123)( 89,122)( 90,121)( 91,120)( 92,119)( 93,118)( 94,117)
( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(126,131)(127,135)
(128,134)(129,133)(130,132)(136,150)(137,149)(138,148)(139,147)(140,146)
(141,145)(142,144)(151,181)(152,185)(153,184)(154,183)(155,182)(156,176)
(157,180)(158,179)(159,178)(160,177)(161,200)(162,199)(163,198)(164,197)
(165,196)(166,195)(167,194)(168,193)(169,192)(170,191)(171,190)(172,189)
(173,188)(174,187)(175,186)(201,206)(202,210)(203,209)(204,208)(205,207)
(211,225)(212,224)(213,223)(214,222)(215,221)(216,220)(217,219)(226,256)
(227,260)(228,259)(229,258)(230,257)(231,251)(232,255)(233,254)(234,253)
(235,252)(236,275)(237,274)(238,273)(239,272)(240,271)(241,270)(242,269)
(243,268)(244,267)(245,266)(246,265)(247,264)(248,263)(249,262)(250,261)
(276,281)(277,285)(278,284)(279,283)(280,282)(286,300)(287,299)(288,298)
(289,297)(290,296)(291,295)(292,294);;
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*s0*s1*s0*s1*s0*s1, 
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*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*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*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*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*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)!(151,226)(152,227)(153,228)(154,229)(155,230)(156,231)(157,232)
(158,233)(159,234)(160,235)(161,236)(162,237)(163,238)(164,239)(165,240)
(166,241)(167,242)(168,243)(169,244)(170,245)(171,246)(172,247)(173,248)
(174,249)(175,250)(176,251)(177,252)(178,253)(179,254)(180,255)(181,256)
(182,257)(183,258)(184,259)(185,260)(186,261)(187,262)(188,263)(189,264)
(190,265)(191,266)(192,267)(193,268)(194,269)(195,270)(196,271)(197,272)
(198,273)(199,274)(200,275)(201,276)(202,277)(203,278)(204,279)(205,280)
(206,281)(207,282)(208,283)(209,284)(210,285)(211,286)(212,287)(213,288)
(214,289)(215,290)(216,291)(217,292)(218,293)(219,294)(220,295)(221,296)
(222,297)(223,298)(224,299)(225,300);
s1 := Sym(300)!(  1,151)(  2,155)(  3,154)(  4,153)(  5,152)(  6,175)(  7,174)
(  8,173)(  9,172)( 10,171)( 11,170)( 12,169)( 13,168)( 14,167)( 15,166)
( 16,165)( 17,164)( 18,163)( 19,162)( 20,161)( 21,160)( 22,159)( 23,158)
( 24,157)( 25,156)( 26,201)( 27,205)( 28,204)( 29,203)( 30,202)( 31,225)
( 32,224)( 33,223)( 34,222)( 35,221)( 36,220)( 37,219)( 38,218)( 39,217)
( 40,216)( 41,215)( 42,214)( 43,213)( 44,212)( 45,211)( 46,210)( 47,209)
( 48,208)( 49,207)( 50,206)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)
( 56,200)( 57,199)( 58,198)( 59,197)( 60,196)( 61,195)( 62,194)( 63,193)
( 64,192)( 65,191)( 66,190)( 67,189)( 68,188)( 69,187)( 70,186)( 71,185)
( 72,184)( 73,183)( 74,182)( 75,181)( 76,226)( 77,230)( 78,229)( 79,228)
( 80,227)( 81,250)( 82,249)( 83,248)( 84,247)( 85,246)( 86,245)( 87,244)
( 88,243)( 89,242)( 90,241)( 91,240)( 92,239)( 93,238)( 94,237)( 95,236)
( 96,235)( 97,234)( 98,233)( 99,232)(100,231)(101,276)(102,280)(103,279)
(104,278)(105,277)(106,300)(107,299)(108,298)(109,297)(110,296)(111,295)
(112,294)(113,293)(114,292)(115,291)(116,290)(117,289)(118,288)(119,287)
(120,286)(121,285)(122,284)(123,283)(124,282)(125,281)(126,251)(127,255)
(128,254)(129,253)(130,252)(131,275)(132,274)(133,273)(134,272)(135,271)
(136,270)(137,269)(138,268)(139,267)(140,266)(141,265)(142,264)(143,263)
(144,262)(145,261)(146,260)(147,259)(148,258)(149,257)(150,256);
s2 := Sym(300)!(  1, 31)(  2, 35)(  3, 34)(  4, 33)(  5, 32)(  6, 26)(  7, 30)
(  8, 29)(  9, 28)( 10, 27)( 11, 50)( 12, 49)( 13, 48)( 14, 47)( 15, 46)
( 16, 45)( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 38)
( 24, 37)( 25, 36)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 75)
( 62, 74)( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 76,106)( 77,110)
( 78,109)( 79,108)( 80,107)( 81,101)( 82,105)( 83,104)( 84,103)( 85,102)
( 86,125)( 87,124)( 88,123)( 89,122)( 90,121)( 91,120)( 92,119)( 93,118)
( 94,117)( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(126,131)
(127,135)(128,134)(129,133)(130,132)(136,150)(137,149)(138,148)(139,147)
(140,146)(141,145)(142,144)(151,181)(152,185)(153,184)(154,183)(155,182)
(156,176)(157,180)(158,179)(159,178)(160,177)(161,200)(162,199)(163,198)
(164,197)(165,196)(166,195)(167,194)(168,193)(169,192)(170,191)(171,190)
(172,189)(173,188)(174,187)(175,186)(201,206)(202,210)(203,209)(204,208)
(205,207)(211,225)(212,224)(213,223)(214,222)(215,221)(216,220)(217,219)
(226,256)(227,260)(228,259)(229,258)(230,257)(231,251)(232,255)(233,254)
(234,253)(235,252)(236,275)(237,274)(238,273)(239,272)(240,271)(241,270)
(242,269)(243,268)(244,267)(245,266)(246,265)(247,264)(248,263)(249,262)
(250,261)(276,281)(277,285)(278,284)(279,283)(280,282)(286,300)(287,299)
(288,298)(289,297)(290,296)(291,295)(292,294);
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*s0*s1*s0*s1*s0*s1, 
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*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*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*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*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*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