Polytope of Type {30,30}

Play with this polytope as a twisty puzzle

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.
Irregular Quotients (of which this is a minimal cover):
   None.

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*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 ];;
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*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 >;
References : None.
to this polytope

Twisty Puzzle