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# Polytope of Type {30,30}

Atlas Canonical Name : {30,30}*1800g
Also Known As : {30,30|2}. if this polytope has another 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 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Dual
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) :
3-fold quotients : {10,30}*600b, {30,10}*600b
5-fold quotients : {6,30}*360b, {30,6}*360b
9-fold quotients : {10,10}*200a
15-fold quotients : {6,10}*120, {10,6}*120, {2,30}*120, {30,2}*120
25-fold quotients : {6,6}*72a
30-fold quotients : {2,15}*60, {15,2}*60
45-fold quotients : {2,10}*40, {10,2}*40
75-fold quotients : {2,6}*24, {6,2}*24
90-fold quotients : {2,5}*20, {5,2}*20
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)(  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)(  2,257)(  3,258)(  4,259)(  5,260)(  6,251)(  7,252)(  8,253)
(  9,254)( 10,255)( 11,271)( 12,272)( 13,273)( 14,274)( 15,275)( 16,266)
( 17,267)( 18,268)( 19,269)( 20,270)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,231)( 27,232)( 28,233)( 29,234)( 30,235)( 31,226)( 32,227)
( 33,228)( 34,229)( 35,230)( 36,246)( 37,247)( 38,248)( 39,249)( 40,250)
( 41,241)( 42,242)( 43,243)( 44,244)( 45,245)( 46,236)( 47,237)( 48,238)
( 49,239)( 50,240)( 51,281)( 52,282)( 53,283)( 54,284)( 55,285)( 56,276)
( 57,277)( 58,278)( 59,279)( 60,280)( 61,296)( 62,297)( 63,298)( 64,299)
( 65,300)( 66,291)( 67,292)( 68,293)( 69,294)( 70,295)( 71,286)( 72,287)
( 73,288)( 74,289)( 75,290)( 76,331)( 77,332)( 78,333)( 79,334)( 80,335)
( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,346)( 87,347)( 88,348)
( 89,349)( 90,350)( 91,341)( 92,342)( 93,343)( 94,344)( 95,345)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,306)(102,307)(103,308)(104,309)
(105,310)(106,301)(107,302)(108,303)(109,304)(110,305)(111,321)(112,322)
(113,323)(114,324)(115,325)(116,316)(117,317)(118,318)(119,319)(120,320)
(121,311)(122,312)(123,313)(124,314)(125,315)(126,356)(127,357)(128,358)
(129,359)(130,360)(131,351)(132,352)(133,353)(134,354)(135,355)(136,371)
(137,372)(138,373)(139,374)(140,375)(141,366)(142,367)(143,368)(144,369)
(145,370)(146,361)(147,362)(148,363)(149,364)(150,365)(151,406)(152,407)
(153,408)(154,409)(155,410)(156,401)(157,402)(158,403)(159,404)(160,405)
(161,421)(162,422)(163,423)(164,424)(165,425)(166,416)(167,417)(168,418)
(169,419)(170,420)(171,411)(172,412)(173,413)(174,414)(175,415)(176,381)
(177,382)(178,383)(179,384)(180,385)(181,376)(182,377)(183,378)(184,379)
(185,380)(186,396)(187,397)(188,398)(189,399)(190,400)(191,391)(192,392)
(193,393)(194,394)(195,395)(196,386)(197,387)(198,388)(199,389)(200,390)
(201,431)(202,432)(203,433)(204,434)(205,435)(206,426)(207,427)(208,428)
(209,429)(210,430)(211,446)(212,447)(213,448)(214,449)(215,450)(216,441)
(217,442)(218,443)(219,444)(220,445)(221,436)(222,437)(223,438)(224,439)
(225,440);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)(  2,257)(  3,258)(  4,259)(  5,260)(  6,251)(  7,252)
(  8,253)(  9,254)( 10,255)( 11,271)( 12,272)( 13,273)( 14,274)( 15,275)
( 16,266)( 17,267)( 18,268)( 19,269)( 20,270)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,231)( 27,232)( 28,233)( 29,234)( 30,235)( 31,226)
( 32,227)( 33,228)( 34,229)( 35,230)( 36,246)( 37,247)( 38,248)( 39,249)
( 40,250)( 41,241)( 42,242)( 43,243)( 44,244)( 45,245)( 46,236)( 47,237)
( 48,238)( 49,239)( 50,240)( 51,281)( 52,282)( 53,283)( 54,284)( 55,285)
( 56,276)( 57,277)( 58,278)( 59,279)( 60,280)( 61,296)( 62,297)( 63,298)
( 64,299)( 65,300)( 66,291)( 67,292)( 68,293)( 69,294)( 70,295)( 71,286)
( 72,287)( 73,288)( 74,289)( 75,290)( 76,331)( 77,332)( 78,333)( 79,334)
( 80,335)( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,346)( 87,347)
( 88,348)( 89,349)( 90,350)( 91,341)( 92,342)( 93,343)( 94,344)( 95,345)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,306)(102,307)(103,308)
(104,309)(105,310)(106,301)(107,302)(108,303)(109,304)(110,305)(111,321)
(112,322)(113,323)(114,324)(115,325)(116,316)(117,317)(118,318)(119,319)
(120,320)(121,311)(122,312)(123,313)(124,314)(125,315)(126,356)(127,357)
(128,358)(129,359)(130,360)(131,351)(132,352)(133,353)(134,354)(135,355)
(136,371)(137,372)(138,373)(139,374)(140,375)(141,366)(142,367)(143,368)
(144,369)(145,370)(146,361)(147,362)(148,363)(149,364)(150,365)(151,406)
(152,407)(153,408)(154,409)(155,410)(156,401)(157,402)(158,403)(159,404)
(160,405)(161,421)(162,422)(163,423)(164,424)(165,425)(166,416)(167,417)
(168,418)(169,419)(170,420)(171,411)(172,412)(173,413)(174,414)(175,415)
(176,381)(177,382)(178,383)(179,384)(180,385)(181,376)(182,377)(183,378)
(184,379)(185,380)(186,396)(187,397)(188,398)(189,399)(190,400)(191,391)
(192,392)(193,393)(194,394)(195,395)(196,386)(197,387)(198,388)(199,389)
(200,390)(201,431)(202,432)(203,433)(204,434)(205,435)(206,426)(207,427)
(208,428)(209,429)(210,430)(211,446)(212,447)(213,448)(214,449)(215,450)
(216,441)(217,442)(218,443)(219,444)(220,445)(221,436)(222,437)(223,438)
(224,439)(225,440);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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