Part of the Atlas of Small Regular Polytopes

Polytope of Type {114,6}

Atlas Canonical Name {114,6}*1824

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1824,1245)
Rank
3
Schläfli Type
{114,6}
Vertices, edges, …
152, 456, 8
Order of s0s1s2
76
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

12-fold

19-fold

24-fold

38-fold

76-fold

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

References

None.

to this polytope.

Twisty Puzzle