Polytope of Type {30,30}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,30}*1800i
if this polytope has a name.
Group : SmallGroup(1800,736)
Rank : 3
Schlafli Type : {30,30}
Number of vertices, edges, etc : 30, 450, 30
Order of s0s1s2 : 30
Order of s0s1s2s1 : 30
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 : {15,30}*900
3-fold quotients : {30,10}*600c
5-fold quotients : {30,6}*360c
6-fold quotients : {15,10}*300
9-fold quotients : {10,10}*200c
10-fold quotients : {15,6}*180
15-fold quotients : {30,2}*120
18-fold quotients : {5,10}*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, 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)( 76,151)( 77,155)( 78,154)
( 79,153)( 80,152)( 81,171)( 82,175)( 83,174)( 84,173)( 85,172)( 86,166)
( 87,170)( 88,169)( 89,168)( 90,167)( 91,161)( 92,165)( 93,164)( 94,163)
( 95,162)( 96,156)( 97,160)( 98,159)( 99,158)(100,157)(101,201)(102,205)
(103,204)(104,203)(105,202)(106,221)(107,225)(108,224)(109,223)(110,222)
(111,216)(112,220)(113,219)(114,218)(115,217)(116,211)(117,215)(118,214)
(119,213)(120,212)(121,206)(122,210)(123,209)(124,208)(125,207)(126,176)
(127,180)(128,179)(129,178)(130,177)(131,196)(132,200)(133,199)(134,198)
(135,197)(136,191)(137,195)(138,194)(139,193)(140,192)(141,186)(142,190)
(143,189)(144,188)(145,187)(146,181)(147,185)(148,184)(149,183)(150,182)
(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)(301,376)(302,380)(303,379)
(304,378)(305,377)(306,396)(307,400)(308,399)(309,398)(310,397)(311,391)
(312,395)(313,394)(314,393)(315,392)(316,386)(317,390)(318,389)(319,388)
(320,387)(321,381)(322,385)(323,384)(324,383)(325,382)(326,426)(327,430)
(328,429)(329,428)(330,427)(331,446)(332,450)(333,449)(334,448)(335,447)
(336,441)(337,445)(338,444)(339,443)(340,442)(341,436)(342,440)(343,439)
(344,438)(345,437)(346,431)(347,435)(348,434)(349,433)(350,432)(351,401)
(352,405)(353,404)(354,403)(355,402)(356,421)(357,425)(358,424)(359,423)
(360,422)(361,416)(362,420)(363,419)(364,418)(365,417)(366,411)(367,415)
(368,414)(369,413)(370,412)(371,406)(372,410)(373,409)(374,408)(375,407);;
s1 := ( 1,332)( 2,331)( 3,335)( 4,334)( 5,333)( 6,327)( 7,326)( 8,330)
( 9,329)( 10,328)( 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)( 26,307)( 27,306)( 28,310)( 29,309)( 30,308)( 31,302)( 32,301)
( 33,305)( 34,304)( 35,303)( 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)( 51,357)( 52,356)( 53,360)( 54,359)( 55,358)( 56,352)
( 57,351)( 58,355)( 59,354)( 60,353)( 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)( 76,257)( 77,256)( 78,260)( 79,259)( 80,258)
( 81,252)( 82,251)( 83,255)( 84,254)( 85,253)( 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)(101,232)(102,231)(103,235)(104,234)
(105,233)(106,227)(107,226)(108,230)(109,229)(110,228)(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)(126,282)(127,281)(128,285)
(129,284)(130,283)(131,277)(132,276)(133,280)(134,279)(135,278)(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)(151,407)(152,406)
(153,410)(154,409)(155,408)(156,402)(157,401)(158,405)(159,404)(160,403)
(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)(176,382)
(177,381)(178,385)(179,384)(180,383)(181,377)(182,376)(183,380)(184,379)
(185,378)(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)
(201,432)(202,431)(203,435)(204,434)(205,433)(206,427)(207,426)(208,430)
(209,429)(210,428)(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 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 76,151)( 77,155)
( 78,154)( 79,153)( 80,152)( 81,156)( 82,160)( 83,159)( 84,158)( 85,157)
( 86,161)( 87,165)( 88,164)( 89,163)( 90,162)( 91,166)( 92,170)( 93,169)
( 94,168)( 95,167)( 96,171)( 97,175)( 98,174)( 99,173)(100,172)(101,176)
(102,180)(103,179)(104,178)(105,177)(106,181)(107,185)(108,184)(109,183)
(110,182)(111,186)(112,190)(113,189)(114,188)(115,187)(116,191)(117,195)
(118,194)(119,193)(120,192)(121,196)(122,200)(123,199)(124,198)(125,197)
(126,201)(127,205)(128,204)(129,203)(130,202)(131,206)(132,210)(133,209)
(134,208)(135,207)(136,211)(137,215)(138,214)(139,213)(140,212)(141,216)
(142,220)(143,219)(144,218)(145,217)(146,221)(147,225)(148,224)(149,223)
(150,222)(227,230)(228,229)(232,235)(233,234)(237,240)(238,239)(242,245)
(243,244)(247,250)(248,249)(252,255)(253,254)(257,260)(258,259)(262,265)
(263,264)(267,270)(268,269)(272,275)(273,274)(277,280)(278,279)(282,285)
(283,284)(287,290)(288,289)(292,295)(293,294)(297,300)(298,299)(301,376)
(302,380)(303,379)(304,378)(305,377)(306,381)(307,385)(308,384)(309,383)
(310,382)(311,386)(312,390)(313,389)(314,388)(315,387)(316,391)(317,395)
(318,394)(319,393)(320,392)(321,396)(322,400)(323,399)(324,398)(325,397)
(326,401)(327,405)(328,404)(329,403)(330,402)(331,406)(332,410)(333,409)
(334,408)(335,407)(336,411)(337,415)(338,414)(339,413)(340,412)(341,416)
(342,420)(343,419)(344,418)(345,417)(346,421)(347,425)(348,424)(349,423)
(350,422)(351,426)(352,430)(353,429)(354,428)(355,427)(356,431)(357,435)
(358,434)(359,433)(360,432)(361,436)(362,440)(363,439)(364,438)(365,437)
(366,441)(367,445)(368,444)(369,443)(370,442)(371,446)(372,450)(373,449)
(374,448)(375,447);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*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)( 76,151)( 77,155)
( 78,154)( 79,153)( 80,152)( 81,171)( 82,175)( 83,174)( 84,173)( 85,172)
( 86,166)( 87,170)( 88,169)( 89,168)( 90,167)( 91,161)( 92,165)( 93,164)
( 94,163)( 95,162)( 96,156)( 97,160)( 98,159)( 99,158)(100,157)(101,201)
(102,205)(103,204)(104,203)(105,202)(106,221)(107,225)(108,224)(109,223)
(110,222)(111,216)(112,220)(113,219)(114,218)(115,217)(116,211)(117,215)
(118,214)(119,213)(120,212)(121,206)(122,210)(123,209)(124,208)(125,207)
(126,176)(127,180)(128,179)(129,178)(130,177)(131,196)(132,200)(133,199)
(134,198)(135,197)(136,191)(137,195)(138,194)(139,193)(140,192)(141,186)
(142,190)(143,189)(144,188)(145,187)(146,181)(147,185)(148,184)(149,183)
(150,182)(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)(301,376)(302,380)
(303,379)(304,378)(305,377)(306,396)(307,400)(308,399)(309,398)(310,397)
(311,391)(312,395)(313,394)(314,393)(315,392)(316,386)(317,390)(318,389)
(319,388)(320,387)(321,381)(322,385)(323,384)(324,383)(325,382)(326,426)
(327,430)(328,429)(329,428)(330,427)(331,446)(332,450)(333,449)(334,448)
(335,447)(336,441)(337,445)(338,444)(339,443)(340,442)(341,436)(342,440)
(343,439)(344,438)(345,437)(346,431)(347,435)(348,434)(349,433)(350,432)
(351,401)(352,405)(353,404)(354,403)(355,402)(356,421)(357,425)(358,424)
(359,423)(360,422)(361,416)(362,420)(363,419)(364,418)(365,417)(366,411)
(367,415)(368,414)(369,413)(370,412)(371,406)(372,410)(373,409)(374,408)
(375,407);
s1 := Sym(450)!( 1,332)( 2,331)( 3,335)( 4,334)( 5,333)( 6,327)( 7,326)
( 8,330)( 9,329)( 10,328)( 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)( 26,307)( 27,306)( 28,310)( 29,309)( 30,308)( 31,302)
( 32,301)( 33,305)( 34,304)( 35,303)( 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)( 51,357)( 52,356)( 53,360)( 54,359)( 55,358)
( 56,352)( 57,351)( 58,355)( 59,354)( 60,353)( 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)( 76,257)( 77,256)( 78,260)( 79,259)
( 80,258)( 81,252)( 82,251)( 83,255)( 84,254)( 85,253)( 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)(101,232)(102,231)(103,235)
(104,234)(105,233)(106,227)(107,226)(108,230)(109,229)(110,228)(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)(126,282)(127,281)
(128,285)(129,284)(130,283)(131,277)(132,276)(133,280)(134,279)(135,278)
(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)(151,407)
(152,406)(153,410)(154,409)(155,408)(156,402)(157,401)(158,405)(159,404)
(160,403)(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)
(176,382)(177,381)(178,385)(179,384)(180,383)(181,377)(182,376)(183,380)
(184,379)(185,378)(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)(201,432)(202,431)(203,435)(204,434)(205,433)(206,427)(207,426)
(208,430)(209,429)(210,428)(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)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 76,151)
( 77,155)( 78,154)( 79,153)( 80,152)( 81,156)( 82,160)( 83,159)( 84,158)
( 85,157)( 86,161)( 87,165)( 88,164)( 89,163)( 90,162)( 91,166)( 92,170)
( 93,169)( 94,168)( 95,167)( 96,171)( 97,175)( 98,174)( 99,173)(100,172)
(101,176)(102,180)(103,179)(104,178)(105,177)(106,181)(107,185)(108,184)
(109,183)(110,182)(111,186)(112,190)(113,189)(114,188)(115,187)(116,191)
(117,195)(118,194)(119,193)(120,192)(121,196)(122,200)(123,199)(124,198)
(125,197)(126,201)(127,205)(128,204)(129,203)(130,202)(131,206)(132,210)
(133,209)(134,208)(135,207)(136,211)(137,215)(138,214)(139,213)(140,212)
(141,216)(142,220)(143,219)(144,218)(145,217)(146,221)(147,225)(148,224)
(149,223)(150,222)(227,230)(228,229)(232,235)(233,234)(237,240)(238,239)
(242,245)(243,244)(247,250)(248,249)(252,255)(253,254)(257,260)(258,259)
(262,265)(263,264)(267,270)(268,269)(272,275)(273,274)(277,280)(278,279)
(282,285)(283,284)(287,290)(288,289)(292,295)(293,294)(297,300)(298,299)
(301,376)(302,380)(303,379)(304,378)(305,377)(306,381)(307,385)(308,384)
(309,383)(310,382)(311,386)(312,390)(313,389)(314,388)(315,387)(316,391)
(317,395)(318,394)(319,393)(320,392)(321,396)(322,400)(323,399)(324,398)
(325,397)(326,401)(327,405)(328,404)(329,403)(330,402)(331,406)(332,410)
(333,409)(334,408)(335,407)(336,411)(337,415)(338,414)(339,413)(340,412)
(341,416)(342,420)(343,419)(344,418)(345,417)(346,421)(347,425)(348,424)
(349,423)(350,422)(351,426)(352,430)(353,429)(354,428)(355,427)(356,431)
(357,435)(358,434)(359,433)(360,432)(361,436)(362,440)(363,439)(364,438)
(365,437)(366,441)(367,445)(368,444)(369,443)(370,442)(371,446)(372,450)
(373,449)(374,448)(375,447);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope