Polytope of Type {30,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*1800c
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 : 30
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 : {30,3}*900
3-fold quotients : {10,6}*600b
6-fold quotients : {10,3}*300
25-fold quotients : {6,6}*72b
50-fold quotients : {6,3}*36
75-fold quotients : {2,6}*24
150-fold quotients : {2,3}*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)( 2,307)( 3,313)( 4,319)( 5,325)( 6,321)( 7,302)( 8,308)
( 9,314)( 10,320)( 11,316)( 12,322)( 13,303)( 14,309)( 15,315)( 16,311)
( 17,317)( 18,323)( 19,304)( 20,310)( 21,306)( 22,312)( 23,318)( 24,324)
( 25,305)( 26,351)( 27,357)( 28,363)( 29,369)( 30,375)( 31,371)( 32,352)
( 33,358)( 34,364)( 35,370)( 36,366)( 37,372)( 38,353)( 39,359)( 40,365)
( 41,361)( 42,367)( 43,373)( 44,354)( 45,360)( 46,356)( 47,362)( 48,368)
( 49,374)( 50,355)( 51,326)( 52,332)( 53,338)( 54,344)( 55,350)( 56,346)
( 57,327)( 58,333)( 59,339)( 60,345)( 61,341)( 62,347)( 63,328)( 64,334)
( 65,340)( 66,336)( 67,342)( 68,348)( 69,329)( 70,335)( 71,331)( 72,337)
( 73,343)( 74,349)( 75,330)( 76,226)( 77,232)( 78,238)( 79,244)( 80,250)
( 81,246)( 82,227)( 83,233)( 84,239)( 85,245)( 86,241)( 87,247)( 88,228)
( 89,234)( 90,240)( 91,236)( 92,242)( 93,248)( 94,229)( 95,235)( 96,231)
( 97,237)( 98,243)( 99,249)(100,230)(101,276)(102,282)(103,288)(104,294)
(105,300)(106,296)(107,277)(108,283)(109,289)(110,295)(111,291)(112,297)
(113,278)(114,284)(115,290)(116,286)(117,292)(118,298)(119,279)(120,285)
(121,281)(122,287)(123,293)(124,299)(125,280)(126,251)(127,257)(128,263)
(129,269)(130,275)(131,271)(132,252)(133,258)(134,264)(135,270)(136,266)
(137,272)(138,253)(139,259)(140,265)(141,261)(142,267)(143,273)(144,254)
(145,260)(146,256)(147,262)(148,268)(149,274)(150,255)(151,376)(152,382)
(153,388)(154,394)(155,400)(156,396)(157,377)(158,383)(159,389)(160,395)
(161,391)(162,397)(163,378)(164,384)(165,390)(166,386)(167,392)(168,398)
(169,379)(170,385)(171,381)(172,387)(173,393)(174,399)(175,380)(176,426)
(177,432)(178,438)(179,444)(180,450)(181,446)(182,427)(183,433)(184,439)
(185,445)(186,441)(187,447)(188,428)(189,434)(190,440)(191,436)(192,442)
(193,448)(194,429)(195,435)(196,431)(197,437)(198,443)(199,449)(200,430)
(201,401)(202,407)(203,413)(204,419)(205,425)(206,421)(207,402)(208,408)
(209,414)(210,420)(211,416)(212,422)(213,403)(214,409)(215,415)(216,411)
(217,417)(218,423)(219,404)(220,410)(221,406)(222,412)(223,418)(224,424)
(225,405);;
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*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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, 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)( 2,307)( 3,313)( 4,319)( 5,325)( 6,321)( 7,302)
( 8,308)( 9,314)( 10,320)( 11,316)( 12,322)( 13,303)( 14,309)( 15,315)
( 16,311)( 17,317)( 18,323)( 19,304)( 20,310)( 21,306)( 22,312)( 23,318)
( 24,324)( 25,305)( 26,351)( 27,357)( 28,363)( 29,369)( 30,375)( 31,371)
( 32,352)( 33,358)( 34,364)( 35,370)( 36,366)( 37,372)( 38,353)( 39,359)
( 40,365)( 41,361)( 42,367)( 43,373)( 44,354)( 45,360)( 46,356)( 47,362)
( 48,368)( 49,374)( 50,355)( 51,326)( 52,332)( 53,338)( 54,344)( 55,350)
( 56,346)( 57,327)( 58,333)( 59,339)( 60,345)( 61,341)( 62,347)( 63,328)
( 64,334)( 65,340)( 66,336)( 67,342)( 68,348)( 69,329)( 70,335)( 71,331)
( 72,337)( 73,343)( 74,349)( 75,330)( 76,226)( 77,232)( 78,238)( 79,244)
( 80,250)( 81,246)( 82,227)( 83,233)( 84,239)( 85,245)( 86,241)( 87,247)
( 88,228)( 89,234)( 90,240)( 91,236)( 92,242)( 93,248)( 94,229)( 95,235)
( 96,231)( 97,237)( 98,243)( 99,249)(100,230)(101,276)(102,282)(103,288)
(104,294)(105,300)(106,296)(107,277)(108,283)(109,289)(110,295)(111,291)
(112,297)(113,278)(114,284)(115,290)(116,286)(117,292)(118,298)(119,279)
(120,285)(121,281)(122,287)(123,293)(124,299)(125,280)(126,251)(127,257)
(128,263)(129,269)(130,275)(131,271)(132,252)(133,258)(134,264)(135,270)
(136,266)(137,272)(138,253)(139,259)(140,265)(141,261)(142,267)(143,273)
(144,254)(145,260)(146,256)(147,262)(148,268)(149,274)(150,255)(151,376)
(152,382)(153,388)(154,394)(155,400)(156,396)(157,377)(158,383)(159,389)
(160,395)(161,391)(162,397)(163,378)(164,384)(165,390)(166,386)(167,392)
(168,398)(169,379)(170,385)(171,381)(172,387)(173,393)(174,399)(175,380)
(176,426)(177,432)(178,438)(179,444)(180,450)(181,446)(182,427)(183,433)
(184,439)(185,445)(186,441)(187,447)(188,428)(189,434)(190,440)(191,436)
(192,442)(193,448)(194,429)(195,435)(196,431)(197,437)(198,443)(199,449)
(200,430)(201,401)(202,407)(203,413)(204,419)(205,425)(206,421)(207,402)
(208,408)(209,414)(210,420)(211,416)(212,422)(213,403)(214,409)(215,415)
(216,411)(217,417)(218,423)(219,404)(220,410)(221,406)(222,412)(223,418)
(224,424)(225,405);
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*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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