Polytope of Type {150,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {150,6}*1800c
if this polytope has a name.
Group : SmallGroup(1800,246)
Rank : 3
Schlafli Type : {150,6}
Number of vertices, edges, etc : 150, 450, 6
Order of s₀s₁s₂ : 150
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {75,6}*900
   3-fold quotients : {150,2}*600
   5-fold quotients : {30,6}*360c
   6-fold quotients : {75,2}*300
   9-fold quotients : {50,2}*200
   10-fold quotients : {15,6}*180
   15-fold quotients : {30,2}*120
   18-fold quotients : {25,2}*100
   25-fold quotients : {6,6}*72c
   30-fold quotients : {15,2}*60
   45-fold quotients : {10,2}*40
   50-fold quotients : {3,6}*36
   75-fold quotients : {6,2}*24
   90-fold quotients : {5,2}*20
   150-fold quotients : {3,2}*12
   225-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  5)(  3,  4)(  6, 22)(  7, 21)(  8, 25)(  9, 24)( 10, 23)( 11, 17)
( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 51)( 27, 55)( 28, 54)( 29, 53)
( 30, 52)( 31, 72)( 32, 71)( 33, 75)( 34, 74)( 35, 73)( 36, 67)( 37, 66)
( 38, 70)( 39, 69)( 40, 68)( 41, 62)( 42, 61)( 43, 65)( 44, 64)( 45, 63)
( 46, 57)( 47, 56)( 48, 60)( 49, 59)( 50, 58)( 76,151)( 77,155)( 78,154)
( 79,153)( 80,152)( 81,172)( 82,171)( 83,175)( 84,174)( 85,173)( 86,167)
( 87,166)( 88,170)( 89,169)( 90,168)( 91,162)( 92,161)( 93,165)( 94,164)
( 95,163)( 96,157)( 97,156)( 98,160)( 99,159)(100,158)(101,201)(102,205)
(103,204)(104,203)(105,202)(106,222)(107,221)(108,225)(109,224)(110,223)
(111,217)(112,216)(113,220)(114,219)(115,218)(116,212)(117,211)(118,215)
(119,214)(120,213)(121,207)(122,206)(123,210)(124,209)(125,208)(126,176)
(127,180)(128,179)(129,178)(130,177)(131,197)(132,196)(133,200)(134,199)
(135,198)(136,192)(137,191)(138,195)(139,194)(140,193)(141,187)(142,186)
(143,190)(144,189)(145,188)(146,182)(147,181)(148,185)(149,184)(150,183)
(227,230)(228,229)(231,247)(232,246)(233,250)(234,249)(235,248)(236,242)
(237,241)(238,245)(239,244)(240,243)(251,276)(252,280)(253,279)(254,278)
(255,277)(256,297)(257,296)(258,300)(259,299)(260,298)(261,292)(262,291)
(263,295)(264,294)(265,293)(266,287)(267,286)(268,290)(269,289)(270,288)
(271,282)(272,281)(273,285)(274,284)(275,283)(301,376)(302,380)(303,379)
(304,378)(305,377)(306,397)(307,396)(308,400)(309,399)(310,398)(311,392)
(312,391)(313,395)(314,394)(315,393)(316,387)(317,386)(318,390)(319,389)
(320,388)(321,382)(322,381)(323,385)(324,384)(325,383)(326,426)(327,430)
(328,429)(329,428)(330,427)(331,447)(332,446)(333,450)(334,449)(335,448)
(336,442)(337,441)(338,445)(339,444)(340,443)(341,437)(342,436)(343,440)
(344,439)(345,438)(346,432)(347,431)(348,435)(349,434)(350,433)(351,401)
(352,405)(353,404)(354,403)(355,402)(356,422)(357,421)(358,425)(359,424)
(360,423)(361,417)(362,416)(363,420)(364,419)(365,418)(366,412)(367,411)
(368,415)(369,414)(370,413)(371,407)(372,406)(373,410)(374,409)(375,408);;
s1 := (  1,331)(  2,335)(  3,334)(  4,333)(  5,332)(  6,326)(  7,330)(  8,329)
(  9,328)( 10,327)( 11,347)( 12,346)( 13,350)( 14,349)( 15,348)( 16,342)
( 17,341)( 18,345)( 19,344)( 20,343)( 21,337)( 22,336)( 23,340)( 24,339)
( 25,338)( 26,306)( 27,310)( 28,309)( 29,308)( 30,307)( 31,301)( 32,305)
( 33,304)( 34,303)( 35,302)( 36,322)( 37,321)( 38,325)( 39,324)( 40,323)
( 41,317)( 42,316)( 43,320)( 44,319)( 45,318)( 46,312)( 47,311)( 48,315)
( 49,314)( 50,313)( 51,356)( 52,360)( 53,359)( 54,358)( 55,357)( 56,351)
( 57,355)( 58,354)( 59,353)( 60,352)( 61,372)( 62,371)( 63,375)( 64,374)
( 65,373)( 66,367)( 67,366)( 68,370)( 69,369)( 70,368)( 71,362)( 72,361)
( 73,365)( 74,364)( 75,363)( 76,256)( 77,260)( 78,259)( 79,258)( 80,257)
( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,272)( 87,271)( 88,275)
( 89,274)( 90,273)( 91,267)( 92,266)( 93,270)( 94,269)( 95,268)( 96,262)
( 97,261)( 98,265)( 99,264)(100,263)(101,231)(102,235)(103,234)(104,233)
(105,232)(106,226)(107,230)(108,229)(109,228)(110,227)(111,247)(112,246)
(113,250)(114,249)(115,248)(116,242)(117,241)(118,245)(119,244)(120,243)
(121,237)(122,236)(123,240)(124,239)(125,238)(126,281)(127,285)(128,284)
(129,283)(130,282)(131,276)(132,280)(133,279)(134,278)(135,277)(136,297)
(137,296)(138,300)(139,299)(140,298)(141,292)(142,291)(143,295)(144,294)
(145,293)(146,287)(147,286)(148,290)(149,289)(150,288)(151,406)(152,410)
(153,409)(154,408)(155,407)(156,401)(157,405)(158,404)(159,403)(160,402)
(161,422)(162,421)(163,425)(164,424)(165,423)(166,417)(167,416)(168,420)
(169,419)(170,418)(171,412)(172,411)(173,415)(174,414)(175,413)(176,381)
(177,385)(178,384)(179,383)(180,382)(181,376)(182,380)(183,379)(184,378)
(185,377)(186,397)(187,396)(188,400)(189,399)(190,398)(191,392)(192,391)
(193,395)(194,394)(195,393)(196,387)(197,386)(198,390)(199,389)(200,388)
(201,431)(202,435)(203,434)(204,433)(205,432)(206,426)(207,430)(208,429)
(209,428)(210,427)(211,447)(212,446)(213,450)(214,449)(215,448)(216,442)
(217,441)(218,445)(219,444)(220,443)(221,437)(222,436)(223,440)(224,439)
(225,438);;
s2 := ( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)( 81,156)( 82,157)( 83,158)
( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)( 89,164)( 90,165)( 91,166)
( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)( 97,172)( 98,173)( 99,174)
(100,175)(101,176)(102,177)(103,178)(104,179)(105,180)(106,181)(107,182)
(108,183)(109,184)(110,185)(111,186)(112,187)(113,188)(114,189)(115,190)
(116,191)(117,192)(118,193)(119,194)(120,195)(121,196)(122,197)(123,198)
(124,199)(125,200)(126,201)(127,202)(128,203)(129,204)(130,205)(131,206)
(132,207)(133,208)(134,209)(135,210)(136,211)(137,212)(138,213)(139,214)
(140,215)(141,216)(142,217)(143,218)(144,219)(145,220)(146,221)(147,222)
(148,223)(149,224)(150,225)(301,376)(302,377)(303,378)(304,379)(305,380)
(306,381)(307,382)(308,383)(309,384)(310,385)(311,386)(312,387)(313,388)
(314,389)(315,390)(316,391)(317,392)(318,393)(319,394)(320,395)(321,396)
(322,397)(323,398)(324,399)(325,400)(326,401)(327,402)(328,403)(329,404)
(330,405)(331,406)(332,407)(333,408)(334,409)(335,410)(336,411)(337,412)
(338,413)(339,414)(340,415)(341,416)(342,417)(343,418)(344,419)(345,420)
(346,421)(347,422)(348,423)(349,424)(350,425)(351,426)(352,427)(353,428)
(354,429)(355,430)(356,431)(357,432)(358,433)(359,434)(360,435)(361,436)
(362,437)(363,438)(364,439)(365,440)(366,441)(367,442)(368,443)(369,444)
(370,445)(371,446)(372,447)(373,448)(374,449)(375,450);;
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*s2*s1*s0*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*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*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*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(450)!(  2,  5)(  3,  4)(  6, 22)(  7, 21)(  8, 25)(  9, 24)( 10, 23)
( 11, 17)( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 51)( 27, 55)( 28, 54)
( 29, 53)( 30, 52)( 31, 72)( 32, 71)( 33, 75)( 34, 74)( 35, 73)( 36, 67)
( 37, 66)( 38, 70)( 39, 69)( 40, 68)( 41, 62)( 42, 61)( 43, 65)( 44, 64)
( 45, 63)( 46, 57)( 47, 56)( 48, 60)( 49, 59)( 50, 58)( 76,151)( 77,155)
( 78,154)( 79,153)( 80,152)( 81,172)( 82,171)( 83,175)( 84,174)( 85,173)
( 86,167)( 87,166)( 88,170)( 89,169)( 90,168)( 91,162)( 92,161)( 93,165)
( 94,164)( 95,163)( 96,157)( 97,156)( 98,160)( 99,159)(100,158)(101,201)
(102,205)(103,204)(104,203)(105,202)(106,222)(107,221)(108,225)(109,224)
(110,223)(111,217)(112,216)(113,220)(114,219)(115,218)(116,212)(117,211)
(118,215)(119,214)(120,213)(121,207)(122,206)(123,210)(124,209)(125,208)
(126,176)(127,180)(128,179)(129,178)(130,177)(131,197)(132,196)(133,200)
(134,199)(135,198)(136,192)(137,191)(138,195)(139,194)(140,193)(141,187)
(142,186)(143,190)(144,189)(145,188)(146,182)(147,181)(148,185)(149,184)
(150,183)(227,230)(228,229)(231,247)(232,246)(233,250)(234,249)(235,248)
(236,242)(237,241)(238,245)(239,244)(240,243)(251,276)(252,280)(253,279)
(254,278)(255,277)(256,297)(257,296)(258,300)(259,299)(260,298)(261,292)
(262,291)(263,295)(264,294)(265,293)(266,287)(267,286)(268,290)(269,289)
(270,288)(271,282)(272,281)(273,285)(274,284)(275,283)(301,376)(302,380)
(303,379)(304,378)(305,377)(306,397)(307,396)(308,400)(309,399)(310,398)
(311,392)(312,391)(313,395)(314,394)(315,393)(316,387)(317,386)(318,390)
(319,389)(320,388)(321,382)(322,381)(323,385)(324,384)(325,383)(326,426)
(327,430)(328,429)(329,428)(330,427)(331,447)(332,446)(333,450)(334,449)
(335,448)(336,442)(337,441)(338,445)(339,444)(340,443)(341,437)(342,436)
(343,440)(344,439)(345,438)(346,432)(347,431)(348,435)(349,434)(350,433)
(351,401)(352,405)(353,404)(354,403)(355,402)(356,422)(357,421)(358,425)
(359,424)(360,423)(361,417)(362,416)(363,420)(364,419)(365,418)(366,412)
(367,411)(368,415)(369,414)(370,413)(371,407)(372,406)(373,410)(374,409)
(375,408);
s1 := Sym(450)!(  1,331)(  2,335)(  3,334)(  4,333)(  5,332)(  6,326)(  7,330)
(  8,329)(  9,328)( 10,327)( 11,347)( 12,346)( 13,350)( 14,349)( 15,348)
( 16,342)( 17,341)( 18,345)( 19,344)( 20,343)( 21,337)( 22,336)( 23,340)
( 24,339)( 25,338)( 26,306)( 27,310)( 28,309)( 29,308)( 30,307)( 31,301)
( 32,305)( 33,304)( 34,303)( 35,302)( 36,322)( 37,321)( 38,325)( 39,324)
( 40,323)( 41,317)( 42,316)( 43,320)( 44,319)( 45,318)( 46,312)( 47,311)
( 48,315)( 49,314)( 50,313)( 51,356)( 52,360)( 53,359)( 54,358)( 55,357)
( 56,351)( 57,355)( 58,354)( 59,353)( 60,352)( 61,372)( 62,371)( 63,375)
( 64,374)( 65,373)( 66,367)( 67,366)( 68,370)( 69,369)( 70,368)( 71,362)
( 72,361)( 73,365)( 74,364)( 75,363)( 76,256)( 77,260)( 78,259)( 79,258)
( 80,257)( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,272)( 87,271)
( 88,275)( 89,274)( 90,273)( 91,267)( 92,266)( 93,270)( 94,269)( 95,268)
( 96,262)( 97,261)( 98,265)( 99,264)(100,263)(101,231)(102,235)(103,234)
(104,233)(105,232)(106,226)(107,230)(108,229)(109,228)(110,227)(111,247)
(112,246)(113,250)(114,249)(115,248)(116,242)(117,241)(118,245)(119,244)
(120,243)(121,237)(122,236)(123,240)(124,239)(125,238)(126,281)(127,285)
(128,284)(129,283)(130,282)(131,276)(132,280)(133,279)(134,278)(135,277)
(136,297)(137,296)(138,300)(139,299)(140,298)(141,292)(142,291)(143,295)
(144,294)(145,293)(146,287)(147,286)(148,290)(149,289)(150,288)(151,406)
(152,410)(153,409)(154,408)(155,407)(156,401)(157,405)(158,404)(159,403)
(160,402)(161,422)(162,421)(163,425)(164,424)(165,423)(166,417)(167,416)
(168,420)(169,419)(170,418)(171,412)(172,411)(173,415)(174,414)(175,413)
(176,381)(177,385)(178,384)(179,383)(180,382)(181,376)(182,380)(183,379)
(184,378)(185,377)(186,397)(187,396)(188,400)(189,399)(190,398)(191,392)
(192,391)(193,395)(194,394)(195,393)(196,387)(197,386)(198,390)(199,389)
(200,388)(201,431)(202,435)(203,434)(204,433)(205,432)(206,426)(207,430)
(208,429)(209,428)(210,427)(211,447)(212,446)(213,450)(214,449)(215,448)
(216,442)(217,441)(218,445)(219,444)(220,443)(221,437)(222,436)(223,440)
(224,439)(225,438);
s2 := Sym(450)!( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)( 81,156)( 82,157)
( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)( 89,164)( 90,165)
( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)( 97,172)( 98,173)
( 99,174)(100,175)(101,176)(102,177)(103,178)(104,179)(105,180)(106,181)
(107,182)(108,183)(109,184)(110,185)(111,186)(112,187)(113,188)(114,189)
(115,190)(116,191)(117,192)(118,193)(119,194)(120,195)(121,196)(122,197)
(123,198)(124,199)(125,200)(126,201)(127,202)(128,203)(129,204)(130,205)
(131,206)(132,207)(133,208)(134,209)(135,210)(136,211)(137,212)(138,213)
(139,214)(140,215)(141,216)(142,217)(143,218)(144,219)(145,220)(146,221)
(147,222)(148,223)(149,224)(150,225)(301,376)(302,377)(303,378)(304,379)
(305,380)(306,381)(307,382)(308,383)(309,384)(310,385)(311,386)(312,387)
(313,388)(314,389)(315,390)(316,391)(317,392)(318,393)(319,394)(320,395)
(321,396)(322,397)(323,398)(324,399)(325,400)(326,401)(327,402)(328,403)
(329,404)(330,405)(331,406)(332,407)(333,408)(334,409)(335,410)(336,411)
(337,412)(338,413)(339,414)(340,415)(341,416)(342,417)(343,418)(344,419)
(345,420)(346,421)(347,422)(348,423)(349,424)(350,425)(351,426)(352,427)
(353,428)(354,429)(355,430)(356,431)(357,432)(358,433)(359,434)(360,435)
(361,436)(362,437)(363,438)(364,439)(365,440)(366,441)(367,442)(368,443)
(369,444)(370,445)(371,446)(372,447)(373,448)(374,449)(375,450);
poly := sub<Sym(450)|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*s2*s1*s0*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*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*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*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