Polytope of Type {30,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*1800d
if this polytope has a name.
Group : SmallGroup(1800,586)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 150, 450, 30
Order of s0s1s2 : 6
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {30,6}*900
3-fold quotients : {10,6}*600a
6-fold quotients : {10,6}*300
25-fold quotients : {6,6}*72a
75-fold quotients : {2,6}*24, {6,2}*24
150-fold quotients : {2,3}*12, {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, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26, 51)( 27, 55)( 28, 54)( 29, 53)
( 30, 52)( 31, 71)( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 66)( 37, 70)
( 38, 69)( 39, 68)( 40, 67)( 41, 61)( 42, 65)( 43, 64)( 44, 63)( 45, 62)
( 46, 56)( 47, 60)( 48, 59)( 49, 58)( 50, 57)( 77, 80)( 78, 79)( 81, 96)
( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)
( 90, 92)(101,126)(102,130)(103,129)(104,128)(105,127)(106,146)(107,150)
(108,149)(109,148)(110,147)(111,141)(112,145)(113,144)(114,143)(115,142)
(116,136)(117,140)(118,139)(119,138)(120,137)(121,131)(122,135)(123,134)
(124,133)(125,132)(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)
(160,172)(161,166)(162,170)(163,169)(164,168)(165,167)(176,201)(177,205)
(178,204)(179,203)(180,202)(181,221)(182,225)(183,224)(184,223)(185,222)
(186,216)(187,220)(188,219)(189,218)(190,217)(191,211)(192,215)(193,214)
(194,213)(195,212)(196,206)(197,210)(198,209)(199,208)(200,207)(227,230)
(228,229)(231,246)(232,250)(233,249)(234,248)(235,247)(236,241)(237,245)
(238,244)(239,243)(240,242)(251,276)(252,280)(253,279)(254,278)(255,277)
(256,296)(257,300)(258,299)(259,298)(260,297)(261,291)(262,295)(263,294)
(264,293)(265,292)(266,286)(267,290)(268,289)(269,288)(270,287)(271,281)
(272,285)(273,284)(274,283)(275,282)(302,305)(303,304)(306,321)(307,325)
(308,324)(309,323)(310,322)(311,316)(312,320)(313,319)(314,318)(315,317)
(326,351)(327,355)(328,354)(329,353)(330,352)(331,371)(332,375)(333,374)
(334,373)(335,372)(336,366)(337,370)(338,369)(339,368)(340,367)(341,361)
(342,365)(343,364)(344,363)(345,362)(346,356)(347,360)(348,359)(349,358)
(350,357)(377,380)(378,379)(381,396)(382,400)(383,399)(384,398)(385,397)
(386,391)(387,395)(388,394)(389,393)(390,392)(401,426)(402,430)(403,429)
(404,428)(405,427)(406,446)(407,450)(408,449)(409,448)(410,447)(411,441)
(412,445)(413,444)(414,443)(415,442)(416,436)(417,440)(418,439)(419,438)
(420,437)(421,431)(422,435)(423,434)(424,433)(425,432);;
s1 := ( 1, 27)( 2, 26)( 3, 30)( 4, 29)( 5, 28)( 6, 33)( 7, 32)( 8, 31)
( 9, 35)( 10, 34)( 11, 39)( 12, 38)( 13, 37)( 14, 36)( 15, 40)( 16, 45)
( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 46)( 22, 50)( 23, 49)( 24, 48)
( 25, 47)( 51, 52)( 53, 55)( 56, 58)( 59, 60)( 61, 64)( 62, 63)( 66, 70)
( 67, 69)( 72, 75)( 73, 74)( 76,177)( 77,176)( 78,180)( 79,179)( 80,178)
( 81,183)( 82,182)( 83,181)( 84,185)( 85,184)( 86,189)( 87,188)( 88,187)
( 89,186)( 90,190)( 91,195)( 92,194)( 93,193)( 94,192)( 95,191)( 96,196)
( 97,200)( 98,199)( 99,198)(100,197)(101,152)(102,151)(103,155)(104,154)
(105,153)(106,158)(107,157)(108,156)(109,160)(110,159)(111,164)(112,163)
(113,162)(114,161)(115,165)(116,170)(117,169)(118,168)(119,167)(120,166)
(121,171)(122,175)(123,174)(124,173)(125,172)(126,202)(127,201)(128,205)
(129,204)(130,203)(131,208)(132,207)(133,206)(134,210)(135,209)(136,214)
(137,213)(138,212)(139,211)(140,215)(141,220)(142,219)(143,218)(144,217)
(145,216)(146,221)(147,225)(148,224)(149,223)(150,222)(226,252)(227,251)
(228,255)(229,254)(230,253)(231,258)(232,257)(233,256)(234,260)(235,259)
(236,264)(237,263)(238,262)(239,261)(240,265)(241,270)(242,269)(243,268)
(244,267)(245,266)(246,271)(247,275)(248,274)(249,273)(250,272)(276,277)
(278,280)(281,283)(284,285)(286,289)(287,288)(291,295)(292,294)(297,300)
(298,299)(301,402)(302,401)(303,405)(304,404)(305,403)(306,408)(307,407)
(308,406)(309,410)(310,409)(311,414)(312,413)(313,412)(314,411)(315,415)
(316,420)(317,419)(318,418)(319,417)(320,416)(321,421)(322,425)(323,424)
(324,423)(325,422)(326,377)(327,376)(328,380)(329,379)(330,378)(331,383)
(332,382)(333,381)(334,385)(335,384)(336,389)(337,388)(338,387)(339,386)
(340,390)(341,395)(342,394)(343,393)(344,392)(345,391)(346,396)(347,400)
(348,399)(349,398)(350,397)(351,427)(352,426)(353,430)(354,429)(355,428)
(356,433)(357,432)(358,431)(359,435)(360,434)(361,439)(362,438)(363,437)
(364,436)(365,440)(366,445)(367,444)(368,443)(369,442)(370,441)(371,446)
(372,450)(373,449)(374,448)(375,447);;
s2 := ( 1,301)( 2,325)( 3,319)( 4,313)( 5,307)( 6,306)( 7,305)( 8,324)
( 9,318)( 10,312)( 11,311)( 12,310)( 13,304)( 14,323)( 15,317)( 16,316)
( 17,315)( 18,309)( 19,303)( 20,322)( 21,321)( 22,320)( 23,314)( 24,308)
( 25,302)( 26,326)( 27,350)( 28,344)( 29,338)( 30,332)( 31,331)( 32,330)
( 33,349)( 34,343)( 35,337)( 36,336)( 37,335)( 38,329)( 39,348)( 40,342)
( 41,341)( 42,340)( 43,334)( 44,328)( 45,347)( 46,346)( 47,345)( 48,339)
( 49,333)( 50,327)( 51,351)( 52,375)( 53,369)( 54,363)( 55,357)( 56,356)
( 57,355)( 58,374)( 59,368)( 60,362)( 61,361)( 62,360)( 63,354)( 64,373)
( 65,367)( 66,366)( 67,365)( 68,359)( 69,353)( 70,372)( 71,371)( 72,370)
( 73,364)( 74,358)( 75,352)( 76,226)( 77,250)( 78,244)( 79,238)( 80,232)
( 81,231)( 82,230)( 83,249)( 84,243)( 85,237)( 86,236)( 87,235)( 88,229)
( 89,248)( 90,242)( 91,241)( 92,240)( 93,234)( 94,228)( 95,247)( 96,246)
( 97,245)( 98,239)( 99,233)(100,227)(101,251)(102,275)(103,269)(104,263)
(105,257)(106,256)(107,255)(108,274)(109,268)(110,262)(111,261)(112,260)
(113,254)(114,273)(115,267)(116,266)(117,265)(118,259)(119,253)(120,272)
(121,271)(122,270)(123,264)(124,258)(125,252)(126,276)(127,300)(128,294)
(129,288)(130,282)(131,281)(132,280)(133,299)(134,293)(135,287)(136,286)
(137,285)(138,279)(139,298)(140,292)(141,291)(142,290)(143,284)(144,278)
(145,297)(146,296)(147,295)(148,289)(149,283)(150,277)(151,376)(152,400)
(153,394)(154,388)(155,382)(156,381)(157,380)(158,399)(159,393)(160,387)
(161,386)(162,385)(163,379)(164,398)(165,392)(166,391)(167,390)(168,384)
(169,378)(170,397)(171,396)(172,395)(173,389)(174,383)(175,377)(176,401)
(177,425)(178,419)(179,413)(180,407)(181,406)(182,405)(183,424)(184,418)
(185,412)(186,411)(187,410)(188,404)(189,423)(190,417)(191,416)(192,415)
(193,409)(194,403)(195,422)(196,421)(197,420)(198,414)(199,408)(200,402)
(201,426)(202,450)(203,444)(204,438)(205,432)(206,431)(207,430)(208,449)
(209,443)(210,437)(211,436)(212,435)(213,429)(214,448)(215,442)(216,441)
(217,440)(218,434)(219,428)(220,447)(221,446)(222,445)(223,439)(224,433)
(225,427);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)
( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26, 51)( 27, 55)( 28, 54)
( 29, 53)( 30, 52)( 31, 71)( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 66)
( 37, 70)( 38, 69)( 39, 68)( 40, 67)( 41, 61)( 42, 65)( 43, 64)( 44, 63)
( 45, 62)( 46, 56)( 47, 60)( 48, 59)( 49, 58)( 50, 57)( 77, 80)( 78, 79)
( 81, 96)( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)
( 89, 93)( 90, 92)(101,126)(102,130)(103,129)(104,128)(105,127)(106,146)
(107,150)(108,149)(109,148)(110,147)(111,141)(112,145)(113,144)(114,143)
(115,142)(116,136)(117,140)(118,139)(119,138)(120,137)(121,131)(122,135)
(123,134)(124,133)(125,132)(152,155)(153,154)(156,171)(157,175)(158,174)
(159,173)(160,172)(161,166)(162,170)(163,169)(164,168)(165,167)(176,201)
(177,205)(178,204)(179,203)(180,202)(181,221)(182,225)(183,224)(184,223)
(185,222)(186,216)(187,220)(188,219)(189,218)(190,217)(191,211)(192,215)
(193,214)(194,213)(195,212)(196,206)(197,210)(198,209)(199,208)(200,207)
(227,230)(228,229)(231,246)(232,250)(233,249)(234,248)(235,247)(236,241)
(237,245)(238,244)(239,243)(240,242)(251,276)(252,280)(253,279)(254,278)
(255,277)(256,296)(257,300)(258,299)(259,298)(260,297)(261,291)(262,295)
(263,294)(264,293)(265,292)(266,286)(267,290)(268,289)(269,288)(270,287)
(271,281)(272,285)(273,284)(274,283)(275,282)(302,305)(303,304)(306,321)
(307,325)(308,324)(309,323)(310,322)(311,316)(312,320)(313,319)(314,318)
(315,317)(326,351)(327,355)(328,354)(329,353)(330,352)(331,371)(332,375)
(333,374)(334,373)(335,372)(336,366)(337,370)(338,369)(339,368)(340,367)
(341,361)(342,365)(343,364)(344,363)(345,362)(346,356)(347,360)(348,359)
(349,358)(350,357)(377,380)(378,379)(381,396)(382,400)(383,399)(384,398)
(385,397)(386,391)(387,395)(388,394)(389,393)(390,392)(401,426)(402,430)
(403,429)(404,428)(405,427)(406,446)(407,450)(408,449)(409,448)(410,447)
(411,441)(412,445)(413,444)(414,443)(415,442)(416,436)(417,440)(418,439)
(419,438)(420,437)(421,431)(422,435)(423,434)(424,433)(425,432);
s1 := Sym(450)!( 1, 27)( 2, 26)( 3, 30)( 4, 29)( 5, 28)( 6, 33)( 7, 32)
( 8, 31)( 9, 35)( 10, 34)( 11, 39)( 12, 38)( 13, 37)( 14, 36)( 15, 40)
( 16, 45)( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 46)( 22, 50)( 23, 49)
( 24, 48)( 25, 47)( 51, 52)( 53, 55)( 56, 58)( 59, 60)( 61, 64)( 62, 63)
( 66, 70)( 67, 69)( 72, 75)( 73, 74)( 76,177)( 77,176)( 78,180)( 79,179)
( 80,178)( 81,183)( 82,182)( 83,181)( 84,185)( 85,184)( 86,189)( 87,188)
( 88,187)( 89,186)( 90,190)( 91,195)( 92,194)( 93,193)( 94,192)( 95,191)
( 96,196)( 97,200)( 98,199)( 99,198)(100,197)(101,152)(102,151)(103,155)
(104,154)(105,153)(106,158)(107,157)(108,156)(109,160)(110,159)(111,164)
(112,163)(113,162)(114,161)(115,165)(116,170)(117,169)(118,168)(119,167)
(120,166)(121,171)(122,175)(123,174)(124,173)(125,172)(126,202)(127,201)
(128,205)(129,204)(130,203)(131,208)(132,207)(133,206)(134,210)(135,209)
(136,214)(137,213)(138,212)(139,211)(140,215)(141,220)(142,219)(143,218)
(144,217)(145,216)(146,221)(147,225)(148,224)(149,223)(150,222)(226,252)
(227,251)(228,255)(229,254)(230,253)(231,258)(232,257)(233,256)(234,260)
(235,259)(236,264)(237,263)(238,262)(239,261)(240,265)(241,270)(242,269)
(243,268)(244,267)(245,266)(246,271)(247,275)(248,274)(249,273)(250,272)
(276,277)(278,280)(281,283)(284,285)(286,289)(287,288)(291,295)(292,294)
(297,300)(298,299)(301,402)(302,401)(303,405)(304,404)(305,403)(306,408)
(307,407)(308,406)(309,410)(310,409)(311,414)(312,413)(313,412)(314,411)
(315,415)(316,420)(317,419)(318,418)(319,417)(320,416)(321,421)(322,425)
(323,424)(324,423)(325,422)(326,377)(327,376)(328,380)(329,379)(330,378)
(331,383)(332,382)(333,381)(334,385)(335,384)(336,389)(337,388)(338,387)
(339,386)(340,390)(341,395)(342,394)(343,393)(344,392)(345,391)(346,396)
(347,400)(348,399)(349,398)(350,397)(351,427)(352,426)(353,430)(354,429)
(355,428)(356,433)(357,432)(358,431)(359,435)(360,434)(361,439)(362,438)
(363,437)(364,436)(365,440)(366,445)(367,444)(368,443)(369,442)(370,441)
(371,446)(372,450)(373,449)(374,448)(375,447);
s2 := Sym(450)!( 1,301)( 2,325)( 3,319)( 4,313)( 5,307)( 6,306)( 7,305)
( 8,324)( 9,318)( 10,312)( 11,311)( 12,310)( 13,304)( 14,323)( 15,317)
( 16,316)( 17,315)( 18,309)( 19,303)( 20,322)( 21,321)( 22,320)( 23,314)
( 24,308)( 25,302)( 26,326)( 27,350)( 28,344)( 29,338)( 30,332)( 31,331)
( 32,330)( 33,349)( 34,343)( 35,337)( 36,336)( 37,335)( 38,329)( 39,348)
( 40,342)( 41,341)( 42,340)( 43,334)( 44,328)( 45,347)( 46,346)( 47,345)
( 48,339)( 49,333)( 50,327)( 51,351)( 52,375)( 53,369)( 54,363)( 55,357)
( 56,356)( 57,355)( 58,374)( 59,368)( 60,362)( 61,361)( 62,360)( 63,354)
( 64,373)( 65,367)( 66,366)( 67,365)( 68,359)( 69,353)( 70,372)( 71,371)
( 72,370)( 73,364)( 74,358)( 75,352)( 76,226)( 77,250)( 78,244)( 79,238)
( 80,232)( 81,231)( 82,230)( 83,249)( 84,243)( 85,237)( 86,236)( 87,235)
( 88,229)( 89,248)( 90,242)( 91,241)( 92,240)( 93,234)( 94,228)( 95,247)
( 96,246)( 97,245)( 98,239)( 99,233)(100,227)(101,251)(102,275)(103,269)
(104,263)(105,257)(106,256)(107,255)(108,274)(109,268)(110,262)(111,261)
(112,260)(113,254)(114,273)(115,267)(116,266)(117,265)(118,259)(119,253)
(120,272)(121,271)(122,270)(123,264)(124,258)(125,252)(126,276)(127,300)
(128,294)(129,288)(130,282)(131,281)(132,280)(133,299)(134,293)(135,287)
(136,286)(137,285)(138,279)(139,298)(140,292)(141,291)(142,290)(143,284)
(144,278)(145,297)(146,296)(147,295)(148,289)(149,283)(150,277)(151,376)
(152,400)(153,394)(154,388)(155,382)(156,381)(157,380)(158,399)(159,393)
(160,387)(161,386)(162,385)(163,379)(164,398)(165,392)(166,391)(167,390)
(168,384)(169,378)(170,397)(171,396)(172,395)(173,389)(174,383)(175,377)
(176,401)(177,425)(178,419)(179,413)(180,407)(181,406)(182,405)(183,424)
(184,418)(185,412)(186,411)(187,410)(188,404)(189,423)(190,417)(191,416)
(192,415)(193,409)(194,403)(195,422)(196,421)(197,420)(198,414)(199,408)
(200,402)(201,426)(202,450)(203,444)(204,438)(205,432)(206,431)(207,430)
(208,449)(209,443)(210,437)(211,436)(212,435)(213,429)(214,448)(215,442)
(216,441)(217,440)(218,434)(219,428)(220,447)(221,446)(222,445)(223,439)
(224,433)(225,427);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope