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