Overview
- Group
- SmallGroup(1800,246)
- Rank
- 3
- Schläfli Type
- {150,6}
- Vertices, edges, …
- 150, 450, 6
- Order of s0s1s2
- 150
- Order of s0s1s2s1
- 2
- Also known as
- {150,6|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
6-fold
9-fold
15-fold
18-fold
25-fold
30-fold
45-fold
75-fold
90-fold
150-fold
225-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
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)( 77, 80)( 78, 79)( 81, 97)( 82, 96)( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)( 90, 93)(101,126)(102,130)(103,129)(104,128)(105,127)(106,147)(107,146)(108,150)(109,149)(110,148)(111,142)(112,141)(113,145)(114,144)(115,143)(116,137)(117,136)(118,140)(119,139)(120,138)(121,132)(122,131)(123,135)(124,134)(125,133)(152,155)(153,154)(156,172)(157,171)(158,175)(159,174)(160,173)(161,167)(162,166)(163,170)(164,169)(165,168)(176,201)(177,205)(178,204)(179,203)(180,202)(181,222)(182,221)(183,225)(184,224)(185,223)(186,217)(187,216)(188,220)(189,219)(190,218)(191,212)(192,211)(193,215)(194,214)(195,213)(196,207)(197,206)(198,210)(199,209)(200,208)(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)(302,305)(303,304)(306,322)(307,321)(308,325)(309,324)(310,323)(311,317)(312,316)(313,320)(314,319)(315,318)(326,351)(327,355)(328,354)(329,353)(330,352)(331,372)(332,371)(333,375)(334,374)(335,373)(336,367)(337,366)(338,370)(339,369)(340,368)(341,362)(342,361)(343,365)(344,364)(345,363)(346,357)(347,356)(348,360)(349,359)(350,358)(377,380)(378,379)(381,397)(382,396)(383,400)(384,399)(385,398)(386,392)(387,391)(388,395)(389,394)(390,393)(401,426)(402,430)(403,429)(404,428)(405,427)(406,447)(407,446)(408,450)(409,449)(410,448)(411,442)(412,441)(413,445)(414,444)(415,443)(416,437)(417,436)(418,440)(419,439)(420,438)(421,432)(422,431)(423,435)(424,434)(425,433);; s1 := ( 1, 31)( 2, 35)( 3, 34)( 4, 33)( 5, 32)( 6, 26)( 7, 30)( 8, 29)( 9, 28)( 10, 27)( 11, 47)( 12, 46)( 13, 50)( 14, 49)( 15, 48)( 16, 42)( 17, 41)( 18, 45)( 19, 44)( 20, 43)( 21, 37)( 22, 36)( 23, 40)( 24, 39)( 25, 38)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 72)( 62, 71)( 63, 75)( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76,181)( 77,185)( 78,184)( 79,183)( 80,182)( 81,176)( 82,180)( 83,179)( 84,178)( 85,177)( 86,197)( 87,196)( 88,200)( 89,199)( 90,198)( 91,192)( 92,191)( 93,195)( 94,194)( 95,193)( 96,187)( 97,186)( 98,190)( 99,189)(100,188)(101,156)(102,160)(103,159)(104,158)(105,157)(106,151)(107,155)(108,154)(109,153)(110,152)(111,172)(112,171)(113,175)(114,174)(115,173)(116,167)(117,166)(118,170)(119,169)(120,168)(121,162)(122,161)(123,165)(124,164)(125,163)(126,206)(127,210)(128,209)(129,208)(130,207)(131,201)(132,205)(133,204)(134,203)(135,202)(136,222)(137,221)(138,225)(139,224)(140,223)(141,217)(142,216)(143,220)(144,219)(145,218)(146,212)(147,211)(148,215)(149,214)(150,213)(226,256)(227,260)(228,259)(229,258)(230,257)(231,251)(232,255)(233,254)(234,253)(235,252)(236,272)(237,271)(238,275)(239,274)(240,273)(241,267)(242,266)(243,270)(244,269)(245,268)(246,262)(247,261)(248,265)(249,264)(250,263)(276,281)(277,285)(278,284)(279,283)(280,282)(286,297)(287,296)(288,300)(289,299)(290,298)(291,292)(293,295)(301,406)(302,410)(303,409)(304,408)(305,407)(306,401)(307,405)(308,404)(309,403)(310,402)(311,422)(312,421)(313,425)(314,424)(315,423)(316,417)(317,416)(318,420)(319,419)(320,418)(321,412)(322,411)(323,415)(324,414)(325,413)(326,381)(327,385)(328,384)(329,383)(330,382)(331,376)(332,380)(333,379)(334,378)(335,377)(336,397)(337,396)(338,400)(339,399)(340,398)(341,392)(342,391)(343,395)(344,394)(345,393)(346,387)(347,386)(348,390)(349,389)(350,388)(351,431)(352,435)(353,434)(354,433)(355,432)(356,426)(357,430)(358,429)(359,428)(360,427)(361,447)(362,446)(363,450)(364,449)(365,448)(366,442)(367,441)(368,445)(369,444)(370,443)(371,437)(372,436)(373,440)(374,439)(375,438);; s2 := ( 1,301)( 2,302)( 3,303)( 4,304)( 5,305)( 6,306)( 7,307)( 8,308)( 9,309)( 10,310)( 11,311)( 12,312)( 13,313)( 14,314)( 15,315)( 16,316)( 17,317)( 18,318)( 19,319)( 20,320)( 21,321)( 22,322)( 23,323)( 24,324)( 25,325)( 26,326)( 27,327)( 28,328)( 29,329)( 30,330)( 31,331)( 32,332)( 33,333)( 34,334)( 35,335)( 36,336)( 37,337)( 38,338)( 39,339)( 40,340)( 41,341)( 42,342)( 43,343)( 44,344)( 45,345)( 46,346)( 47,347)( 48,348)( 49,349)( 50,350)( 51,351)( 52,352)( 53,353)( 54,354)( 55,355)( 56,356)( 57,357)( 58,358)( 59,359)( 60,360)( 61,361)( 62,362)( 63,363)( 64,364)( 65,365)( 66,366)( 67,367)( 68,368)( 69,369)( 70,370)( 71,371)( 72,372)( 73,373)( 74,374)( 75,375)( 76,226)( 77,227)( 78,228)( 79,229)( 80,230)( 81,231)( 82,232)( 83,233)( 84,234)( 85,235)( 86,236)( 87,237)( 88,238)( 89,239)( 90,240)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)( 96,246)( 97,247)( 98,248)( 99,249)(100,250)(101,251)(102,252)(103,253)(104,254)(105,255)(106,256)(107,257)(108,258)(109,259)(110,260)(111,261)(112,262)(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)(120,270)(121,271)(122,272)(123,273)(124,274)(125,275)(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)(151,376)(152,377)(153,378)(154,379)(155,380)(156,381)(157,382)(158,383)(159,384)(160,385)(161,386)(162,387)(163,388)(164,389)(165,390)(166,391)(167,392)(168,393)(169,394)(170,395)(171,396)(172,397)(173,398)(174,399)(175,400)(176,401)(177,402)(178,403)(179,404)(180,405)(181,406)(182,407)(183,408)(184,409)(185,410)(186,411)(187,412)(188,413)(189,414)(190,415)(191,416)(192,417)(193,418)(194,419)(195,420)(196,421)(197,422)(198,423)(199,424)(200,425)(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)(208,433)(209,434)(210,435)(211,436)(212,437)(213,438)(214,439)(215,440)(216,441)(217,442)(218,443)(219,444)(220,445)(221,446)(222,447)(223,448)(224,449)(225,450);; 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, s0*s1*s2*s1*s0*s1*s2*s1,
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 77, 80)( 78, 79)( 81, 97)( 82, 96)( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)( 90, 93)(101,126)(102,130)(103,129)(104,128)(105,127)(106,147)(107,146)(108,150)(109,149)(110,148)(111,142)(112,141)(113,145)(114,144)(115,143)(116,137)(117,136)(118,140)(119,139)(120,138)(121,132)(122,131)(123,135)(124,134)(125,133)(152,155)(153,154)(156,172)(157,171)(158,175)(159,174)(160,173)(161,167)(162,166)(163,170)(164,169)(165,168)(176,201)(177,205)(178,204)(179,203)(180,202)(181,222)(182,221)(183,225)(184,224)(185,223)(186,217)(187,216)(188,220)(189,219)(190,218)(191,212)(192,211)(193,215)(194,214)(195,213)(196,207)(197,206)(198,210)(199,209)(200,208)(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)(302,305)(303,304)(306,322)(307,321)(308,325)(309,324)(310,323)(311,317)(312,316)(313,320)(314,319)(315,318)(326,351)(327,355)(328,354)(329,353)(330,352)(331,372)(332,371)(333,375)(334,374)(335,373)(336,367)(337,366)(338,370)(339,369)(340,368)(341,362)(342,361)(343,365)(344,364)(345,363)(346,357)(347,356)(348,360)(349,359)(350,358)(377,380)(378,379)(381,397)(382,396)(383,400)(384,399)(385,398)(386,392)(387,391)(388,395)(389,394)(390,393)(401,426)(402,430)(403,429)(404,428)(405,427)(406,447)(407,446)(408,450)(409,449)(410,448)(411,442)(412,441)(413,445)(414,444)(415,443)(416,437)(417,436)(418,440)(419,439)(420,438)(421,432)(422,431)(423,435)(424,434)(425,433); s1 := Sym(450)!( 1, 31)( 2, 35)( 3, 34)( 4, 33)( 5, 32)( 6, 26)( 7, 30)( 8, 29)( 9, 28)( 10, 27)( 11, 47)( 12, 46)( 13, 50)( 14, 49)( 15, 48)( 16, 42)( 17, 41)( 18, 45)( 19, 44)( 20, 43)( 21, 37)( 22, 36)( 23, 40)( 24, 39)( 25, 38)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 72)( 62, 71)( 63, 75)( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76,181)( 77,185)( 78,184)( 79,183)( 80,182)( 81,176)( 82,180)( 83,179)( 84,178)( 85,177)( 86,197)( 87,196)( 88,200)( 89,199)( 90,198)( 91,192)( 92,191)( 93,195)( 94,194)( 95,193)( 96,187)( 97,186)( 98,190)( 99,189)(100,188)(101,156)(102,160)(103,159)(104,158)(105,157)(106,151)(107,155)(108,154)(109,153)(110,152)(111,172)(112,171)(113,175)(114,174)(115,173)(116,167)(117,166)(118,170)(119,169)(120,168)(121,162)(122,161)(123,165)(124,164)(125,163)(126,206)(127,210)(128,209)(129,208)(130,207)(131,201)(132,205)(133,204)(134,203)(135,202)(136,222)(137,221)(138,225)(139,224)(140,223)(141,217)(142,216)(143,220)(144,219)(145,218)(146,212)(147,211)(148,215)(149,214)(150,213)(226,256)(227,260)(228,259)(229,258)(230,257)(231,251)(232,255)(233,254)(234,253)(235,252)(236,272)(237,271)(238,275)(239,274)(240,273)(241,267)(242,266)(243,270)(244,269)(245,268)(246,262)(247,261)(248,265)(249,264)(250,263)(276,281)(277,285)(278,284)(279,283)(280,282)(286,297)(287,296)(288,300)(289,299)(290,298)(291,292)(293,295)(301,406)(302,410)(303,409)(304,408)(305,407)(306,401)(307,405)(308,404)(309,403)(310,402)(311,422)(312,421)(313,425)(314,424)(315,423)(316,417)(317,416)(318,420)(319,419)(320,418)(321,412)(322,411)(323,415)(324,414)(325,413)(326,381)(327,385)(328,384)(329,383)(330,382)(331,376)(332,380)(333,379)(334,378)(335,377)(336,397)(337,396)(338,400)(339,399)(340,398)(341,392)(342,391)(343,395)(344,394)(345,393)(346,387)(347,386)(348,390)(349,389)(350,388)(351,431)(352,435)(353,434)(354,433)(355,432)(356,426)(357,430)(358,429)(359,428)(360,427)(361,447)(362,446)(363,450)(364,449)(365,448)(366,442)(367,441)(368,445)(369,444)(370,443)(371,437)(372,436)(373,440)(374,439)(375,438); s2 := Sym(450)!( 1,301)( 2,302)( 3,303)( 4,304)( 5,305)( 6,306)( 7,307)( 8,308)( 9,309)( 10,310)( 11,311)( 12,312)( 13,313)( 14,314)( 15,315)( 16,316)( 17,317)( 18,318)( 19,319)( 20,320)( 21,321)( 22,322)( 23,323)( 24,324)( 25,325)( 26,326)( 27,327)( 28,328)( 29,329)( 30,330)( 31,331)( 32,332)( 33,333)( 34,334)( 35,335)( 36,336)( 37,337)( 38,338)( 39,339)( 40,340)( 41,341)( 42,342)( 43,343)( 44,344)( 45,345)( 46,346)( 47,347)( 48,348)( 49,349)( 50,350)( 51,351)( 52,352)( 53,353)( 54,354)( 55,355)( 56,356)( 57,357)( 58,358)( 59,359)( 60,360)( 61,361)( 62,362)( 63,363)( 64,364)( 65,365)( 66,366)( 67,367)( 68,368)( 69,369)( 70,370)( 71,371)( 72,372)( 73,373)( 74,374)( 75,375)( 76,226)( 77,227)( 78,228)( 79,229)( 80,230)( 81,231)( 82,232)( 83,233)( 84,234)( 85,235)( 86,236)( 87,237)( 88,238)( 89,239)( 90,240)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)( 96,246)( 97,247)( 98,248)( 99,249)(100,250)(101,251)(102,252)(103,253)(104,254)(105,255)(106,256)(107,257)(108,258)(109,259)(110,260)(111,261)(112,262)(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)(120,270)(121,271)(122,272)(123,273)(124,274)(125,275)(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)(151,376)(152,377)(153,378)(154,379)(155,380)(156,381)(157,382)(158,383)(159,384)(160,385)(161,386)(162,387)(163,388)(164,389)(165,390)(166,391)(167,392)(168,393)(169,394)(170,395)(171,396)(172,397)(173,398)(174,399)(175,400)(176,401)(177,402)(178,403)(179,404)(180,405)(181,406)(182,407)(183,408)(184,409)(185,410)(186,411)(187,412)(188,413)(189,414)(190,415)(191,416)(192,417)(193,418)(194,419)(195,420)(196,421)(197,422)(198,423)(199,424)(200,425)(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)(208,433)(209,434)(210,435)(211,436)(212,437)(213,438)(214,439)(215,440)(216,441)(217,442)(218,443)(219,444)(220,445)(221,446)(222,447)(223,448)(224,449)(225,450); 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, s0*s1*s2*s1*s0*s1*s2*s1, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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.