Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,230}

Atlas Canonical Name {4,230}*1840

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1840,160)
Rank
3
Schläfli Type
{4,230}
Vertices, edges, …
4, 460, 230
Order of s0s1s2
460
Order of s0s1s2s1
2
Also known as
{4,230|2}. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

5-fold

10-fold

20-fold

23-fold

46-fold

92-fold

115-fold

230-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := (231,346)(232,347)(233,348)(234,349)(235,350)(236,351)(237,352)(238,353)(239,354)(240,355)(241,356)(242,357)(243,358)(244,359)(245,360)(246,361)(247,362)(248,363)(249,364)(250,365)(251,366)(252,367)(253,368)(254,369)(255,370)(256,371)(257,372)(258,373)(259,374)(260,375)(261,376)(262,377)(263,378)(264,379)(265,380)(266,381)(267,382)(268,383)(269,384)(270,385)(271,386)(272,387)(273,388)(274,389)(275,390)(276,391)(277,392)(278,393)(279,394)(280,395)(281,396)(282,397)(283,398)(284,399)(285,400)(286,401)(287,402)(288,403)(289,404)(290,405)(291,406)(292,407)(293,408)(294,409)(295,410)(296,411)(297,412)(298,413)(299,414)(300,415)(301,416)(302,417)(303,418)(304,419)(305,420)(306,421)(307,422)(308,423)(309,424)(310,425)(311,426)(312,427)(313,428)(314,429)(315,430)(316,431)(317,432)(318,433)(319,434)(320,435)(321,436)(322,437)(323,438)(324,439)(325,440)(326,441)(327,442)(328,443)(329,444)(330,445)(331,446)(332,447)(333,448)(334,449)(335,450)(336,451)(337,452)(338,453)(339,454)(340,455)(341,456)(342,457)(343,458)(344,459)(345,460);;
s1 := (  1,231)(  2,253)(  3,252)(  4,251)(  5,250)(  6,249)(  7,248)(  8,247)(  9,246)( 10,245)( 11,244)( 12,243)( 13,242)( 14,241)( 15,240)( 16,239)( 17,238)( 18,237)( 19,236)( 20,235)( 21,234)( 22,233)( 23,232)( 24,323)( 25,345)( 26,344)( 27,343)( 28,342)( 29,341)( 30,340)( 31,339)( 32,338)( 33,337)( 34,336)( 35,335)( 36,334)( 37,333)( 38,332)( 39,331)( 40,330)( 41,329)( 42,328)( 43,327)( 44,326)( 45,325)( 46,324)( 47,300)( 48,322)( 49,321)( 50,320)( 51,319)( 52,318)( 53,317)( 54,316)( 55,315)( 56,314)( 57,313)( 58,312)( 59,311)( 60,310)( 61,309)( 62,308)( 63,307)( 64,306)( 65,305)( 66,304)( 67,303)( 68,302)( 69,301)( 70,277)( 71,299)( 72,298)( 73,297)( 74,296)( 75,295)( 76,294)( 77,293)( 78,292)( 79,291)( 80,290)( 81,289)( 82,288)( 83,287)( 84,286)( 85,285)( 86,284)( 87,283)( 88,282)( 89,281)( 90,280)( 91,279)( 92,278)( 93,254)( 94,276)( 95,275)( 96,274)( 97,273)( 98,272)( 99,271)(100,270)(101,269)(102,268)(103,267)(104,266)(105,265)(106,264)(107,263)(108,262)(109,261)(110,260)(111,259)(112,258)(113,257)(114,256)(115,255)(116,346)(117,368)(118,367)(119,366)(120,365)(121,364)(122,363)(123,362)(124,361)(125,360)(126,359)(127,358)(128,357)(129,356)(130,355)(131,354)(132,353)(133,352)(134,351)(135,350)(136,349)(137,348)(138,347)(139,438)(140,460)(141,459)(142,458)(143,457)(144,456)(145,455)(146,454)(147,453)(148,452)(149,451)(150,450)(151,449)(152,448)(153,447)(154,446)(155,445)(156,444)(157,443)(158,442)(159,441)(160,440)(161,439)(162,415)(163,437)(164,436)(165,435)(166,434)(167,433)(168,432)(169,431)(170,430)(171,429)(172,428)(173,427)(174,426)(175,425)(176,424)(177,423)(178,422)(179,421)(180,420)(181,419)(182,418)(183,417)(184,416)(185,392)(186,414)(187,413)(188,412)(189,411)(190,410)(191,409)(192,408)(193,407)(194,406)(195,405)(196,404)(197,403)(198,402)(199,401)(200,400)(201,399)(202,398)(203,397)(204,396)(205,395)(206,394)(207,393)(208,369)(209,391)(210,390)(211,389)(212,388)(213,387)(214,386)(215,385)(216,384)(217,383)(218,382)(219,381)(220,380)(221,379)(222,378)(223,377)(224,376)(225,375)(226,374)(227,373)(228,372)(229,371)(230,370);;
s2 := (  1, 25)(  2, 24)(  3, 46)(  4, 45)(  5, 44)(  6, 43)(  7, 42)(  8, 41)(  9, 40)( 10, 39)( 11, 38)( 12, 37)( 13, 36)( 14, 35)( 15, 34)( 16, 33)( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 47, 94)( 48, 93)( 49,115)( 50,114)( 51,113)( 52,112)( 53,111)( 54,110)( 55,109)( 56,108)( 57,107)( 58,106)( 59,105)( 60,104)( 61,103)( 62,102)( 63,101)( 64,100)( 65, 99)( 66, 98)( 67, 97)( 68, 96)( 69, 95)( 70, 71)( 72, 92)( 73, 91)( 74, 90)( 75, 89)( 76, 88)( 77, 87)( 78, 86)( 79, 85)( 80, 84)( 81, 83)(116,140)(117,139)(118,161)(119,160)(120,159)(121,158)(122,157)(123,156)(124,155)(125,154)(126,153)(127,152)(128,151)(129,150)(130,149)(131,148)(132,147)(133,146)(134,145)(135,144)(136,143)(137,142)(138,141)(162,209)(163,208)(164,230)(165,229)(166,228)(167,227)(168,226)(169,225)(170,224)(171,223)(172,222)(173,221)(174,220)(175,219)(176,218)(177,217)(178,216)(179,215)(180,214)(181,213)(182,212)(183,211)(184,210)(185,186)(187,207)(188,206)(189,205)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)(231,255)(232,254)(233,276)(234,275)(235,274)(236,273)(237,272)(238,271)(239,270)(240,269)(241,268)(242,267)(243,266)(244,265)(245,264)(246,263)(247,262)(248,261)(249,260)(250,259)(251,258)(252,257)(253,256)(277,324)(278,323)(279,345)(280,344)(281,343)(282,342)(283,341)(284,340)(285,339)(286,338)(287,337)(288,336)(289,335)(290,334)(291,333)(292,332)(293,331)(294,330)(295,329)(296,328)(297,327)(298,326)(299,325)(300,301)(302,322)(303,321)(304,320)(305,319)(306,318)(307,317)(308,316)(309,315)(310,314)(311,313)(346,370)(347,369)(348,391)(349,390)(350,389)(351,388)(352,387)(353,386)(354,385)(355,384)(356,383)(357,382)(358,381)(359,380)(360,379)(361,378)(362,377)(363,376)(364,375)(365,374)(366,373)(367,372)(368,371)(392,439)(393,438)(394,460)(395,459)(396,458)(397,457)(398,456)(399,455)(400,454)(401,453)(402,452)(403,451)(404,450)(405,449)(406,448)(407,447)(408,446)(409,445)(410,444)(411,443)(412,442)(413,441)(414,440)(415,416)(417,437)(418,436)(419,435)(420,434)(421,433)(422,432)(423,431)(424,430)(425,429)(426,428);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*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*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*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*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*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*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*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*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(460)!(231,346)(232,347)(233,348)(234,349)(235,350)(236,351)(237,352)(238,353)(239,354)(240,355)(241,356)(242,357)(243,358)(244,359)(245,360)(246,361)(247,362)(248,363)(249,364)(250,365)(251,366)(252,367)(253,368)(254,369)(255,370)(256,371)(257,372)(258,373)(259,374)(260,375)(261,376)(262,377)(263,378)(264,379)(265,380)(266,381)(267,382)(268,383)(269,384)(270,385)(271,386)(272,387)(273,388)(274,389)(275,390)(276,391)(277,392)(278,393)(279,394)(280,395)(281,396)(282,397)(283,398)(284,399)(285,400)(286,401)(287,402)(288,403)(289,404)(290,405)(291,406)(292,407)(293,408)(294,409)(295,410)(296,411)(297,412)(298,413)(299,414)(300,415)(301,416)(302,417)(303,418)(304,419)(305,420)(306,421)(307,422)(308,423)(309,424)(310,425)(311,426)(312,427)(313,428)(314,429)(315,430)(316,431)(317,432)(318,433)(319,434)(320,435)(321,436)(322,437)(323,438)(324,439)(325,440)(326,441)(327,442)(328,443)(329,444)(330,445)(331,446)(332,447)(333,448)(334,449)(335,450)(336,451)(337,452)(338,453)(339,454)(340,455)(341,456)(342,457)(343,458)(344,459)(345,460);
s1 := Sym(460)!(  1,231)(  2,253)(  3,252)(  4,251)(  5,250)(  6,249)(  7,248)(  8,247)(  9,246)( 10,245)( 11,244)( 12,243)( 13,242)( 14,241)( 15,240)( 16,239)( 17,238)( 18,237)( 19,236)( 20,235)( 21,234)( 22,233)( 23,232)( 24,323)( 25,345)( 26,344)( 27,343)( 28,342)( 29,341)( 30,340)( 31,339)( 32,338)( 33,337)( 34,336)( 35,335)( 36,334)( 37,333)( 38,332)( 39,331)( 40,330)( 41,329)( 42,328)( 43,327)( 44,326)( 45,325)( 46,324)( 47,300)( 48,322)( 49,321)( 50,320)( 51,319)( 52,318)( 53,317)( 54,316)( 55,315)( 56,314)( 57,313)( 58,312)( 59,311)( 60,310)( 61,309)( 62,308)( 63,307)( 64,306)( 65,305)( 66,304)( 67,303)( 68,302)( 69,301)( 70,277)( 71,299)( 72,298)( 73,297)( 74,296)( 75,295)( 76,294)( 77,293)( 78,292)( 79,291)( 80,290)( 81,289)( 82,288)( 83,287)( 84,286)( 85,285)( 86,284)( 87,283)( 88,282)( 89,281)( 90,280)( 91,279)( 92,278)( 93,254)( 94,276)( 95,275)( 96,274)( 97,273)( 98,272)( 99,271)(100,270)(101,269)(102,268)(103,267)(104,266)(105,265)(106,264)(107,263)(108,262)(109,261)(110,260)(111,259)(112,258)(113,257)(114,256)(115,255)(116,346)(117,368)(118,367)(119,366)(120,365)(121,364)(122,363)(123,362)(124,361)(125,360)(126,359)(127,358)(128,357)(129,356)(130,355)(131,354)(132,353)(133,352)(134,351)(135,350)(136,349)(137,348)(138,347)(139,438)(140,460)(141,459)(142,458)(143,457)(144,456)(145,455)(146,454)(147,453)(148,452)(149,451)(150,450)(151,449)(152,448)(153,447)(154,446)(155,445)(156,444)(157,443)(158,442)(159,441)(160,440)(161,439)(162,415)(163,437)(164,436)(165,435)(166,434)(167,433)(168,432)(169,431)(170,430)(171,429)(172,428)(173,427)(174,426)(175,425)(176,424)(177,423)(178,422)(179,421)(180,420)(181,419)(182,418)(183,417)(184,416)(185,392)(186,414)(187,413)(188,412)(189,411)(190,410)(191,409)(192,408)(193,407)(194,406)(195,405)(196,404)(197,403)(198,402)(199,401)(200,400)(201,399)(202,398)(203,397)(204,396)(205,395)(206,394)(207,393)(208,369)(209,391)(210,390)(211,389)(212,388)(213,387)(214,386)(215,385)(216,384)(217,383)(218,382)(219,381)(220,380)(221,379)(222,378)(223,377)(224,376)(225,375)(226,374)(227,373)(228,372)(229,371)(230,370);
s2 := Sym(460)!(  1, 25)(  2, 24)(  3, 46)(  4, 45)(  5, 44)(  6, 43)(  7, 42)(  8, 41)(  9, 40)( 10, 39)( 11, 38)( 12, 37)( 13, 36)( 14, 35)( 15, 34)( 16, 33)( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 47, 94)( 48, 93)( 49,115)( 50,114)( 51,113)( 52,112)( 53,111)( 54,110)( 55,109)( 56,108)( 57,107)( 58,106)( 59,105)( 60,104)( 61,103)( 62,102)( 63,101)( 64,100)( 65, 99)( 66, 98)( 67, 97)( 68, 96)( 69, 95)( 70, 71)( 72, 92)( 73, 91)( 74, 90)( 75, 89)( 76, 88)( 77, 87)( 78, 86)( 79, 85)( 80, 84)( 81, 83)(116,140)(117,139)(118,161)(119,160)(120,159)(121,158)(122,157)(123,156)(124,155)(125,154)(126,153)(127,152)(128,151)(129,150)(130,149)(131,148)(132,147)(133,146)(134,145)(135,144)(136,143)(137,142)(138,141)(162,209)(163,208)(164,230)(165,229)(166,228)(167,227)(168,226)(169,225)(170,224)(171,223)(172,222)(173,221)(174,220)(175,219)(176,218)(177,217)(178,216)(179,215)(180,214)(181,213)(182,212)(183,211)(184,210)(185,186)(187,207)(188,206)(189,205)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)(231,255)(232,254)(233,276)(234,275)(235,274)(236,273)(237,272)(238,271)(239,270)(240,269)(241,268)(242,267)(243,266)(244,265)(245,264)(246,263)(247,262)(248,261)(249,260)(250,259)(251,258)(252,257)(253,256)(277,324)(278,323)(279,345)(280,344)(281,343)(282,342)(283,341)(284,340)(285,339)(286,338)(287,337)(288,336)(289,335)(290,334)(291,333)(292,332)(293,331)(294,330)(295,329)(296,328)(297,327)(298,326)(299,325)(300,301)(302,322)(303,321)(304,320)(305,319)(306,318)(307,317)(308,316)(309,315)(310,314)(311,313)(346,370)(347,369)(348,391)(349,390)(350,389)(351,388)(352,387)(353,386)(354,385)(355,384)(356,383)(357,382)(358,381)(359,380)(360,379)(361,378)(362,377)(363,376)(364,375)(365,374)(366,373)(367,372)(368,371)(392,439)(393,438)(394,460)(395,459)(396,458)(397,457)(398,456)(399,455)(400,454)(401,453)(402,452)(403,451)(404,450)(405,449)(406,448)(407,447)(408,446)(409,445)(410,444)(411,443)(412,442)(413,441)(414,440)(415,416)(417,437)(418,436)(419,435)(420,434)(421,433)(422,432)(423,431)(424,430)(425,429)(426,428);
poly := sub<Sym(460)|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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*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*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*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*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*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*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*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*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.

Twisty Puzzle