Polytope of Type {142,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {142,6}*1704
Also Known As : {142,6|2}. if this polytope has another name.
Group : SmallGroup(1704,34)
Rank : 3
Schlafli Type : {142,6}
Number of vertices, edges, etc : 142, 426, 6
Order of s0s1s2 : 426
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {142,2}*568
   6-fold quotients : {71,2}*284
   71-fold quotients : {2,6}*24
   142-fold quotients : {2,3}*12
   213-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, 71)(  3, 70)(  4, 69)(  5, 68)(  6, 67)(  7, 66)(  8, 65)(  9, 64)( 10, 63)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 58)( 16, 57)( 17, 56)( 18, 55)( 19, 54)( 20, 53)( 21, 52)( 22, 51)( 23, 50)( 24, 49)( 25, 48)( 26, 47)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 36, 37)( 73,142)( 74,141)( 75,140)( 76,139)( 77,138)( 78,137)( 79,136)( 80,135)( 81,134)( 82,133)( 83,132)( 84,131)( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)( 91,124)( 92,123)( 93,122)( 94,121)( 95,120)( 96,119)( 97,118)( 98,117)( 99,116)(100,115)(101,114)(102,113)(103,112)(104,111)(105,110)(106,109)(107,108)(144,213)(145,212)(146,211)(147,210)(148,209)(149,208)(150,207)(151,206)(152,205)(153,204)(154,203)(155,202)(156,201)(157,200)(158,199)(159,198)(160,197)(161,196)(162,195)(163,194)(164,193)(165,192)(166,191)(167,190)(168,189)(169,188)(170,187)(171,186)(172,185)(173,184)(174,183)(175,182)(176,181)(177,180)(178,179)(215,284)(216,283)(217,282)(218,281)(219,280)(220,279)(221,278)(222,277)(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)(229,270)(230,269)(231,268)(232,267)(233,266)(234,265)(235,264)(236,263)(237,262)(238,261)(239,260)(240,259)(241,258)(242,257)(243,256)(244,255)(245,254)(246,253)(247,252)(248,251)(249,250)(286,355)(287,354)(288,353)(289,352)(290,351)(291,350)(292,349)(293,348)(294,347)(295,346)(296,345)(297,344)(298,343)(299,342)(300,341)(301,340)(302,339)(303,338)(304,337)(305,336)(306,335)(307,334)(308,333)(309,332)(310,331)(311,330)(312,329)(313,328)(314,327)(315,326)(316,325)(317,324)(318,323)(319,322)(320,321)(357,426)(358,425)(359,424)(360,423)(361,422)(362,421)(363,420)(364,419)(365,418)(366,417)(367,416)(368,415)(369,414)(370,413)(371,412)(372,411)(373,410)(374,409)(375,408)(376,407)(377,406)(378,405)(379,404)(380,403)(381,402)(382,401)(383,400)(384,399)(385,398)(386,397)(387,396)(388,395)(389,394)(390,393)(391,392);;
s1 := (  1,  2)(  3, 71)(  4, 70)(  5, 69)(  6, 68)(  7, 67)(  8, 66)(  9, 65)( 10, 64)( 11, 63)( 12, 62)( 13, 61)( 14, 60)( 15, 59)( 16, 58)( 17, 57)( 18, 56)( 19, 55)( 20, 54)( 21, 53)( 22, 52)( 23, 51)( 24, 50)( 25, 49)( 26, 48)( 27, 47)( 28, 46)( 29, 45)( 30, 44)( 31, 43)( 32, 42)( 33, 41)( 34, 40)( 35, 39)( 36, 38)( 72,144)( 73,143)( 74,213)( 75,212)( 76,211)( 77,210)( 78,209)( 79,208)( 80,207)( 81,206)( 82,205)( 83,204)( 84,203)( 85,202)( 86,201)( 87,200)( 88,199)( 89,198)( 90,197)( 91,196)( 92,195)( 93,194)( 94,193)( 95,192)( 96,191)( 97,190)( 98,189)( 99,188)(100,187)(101,186)(102,185)(103,184)(104,183)(105,182)(106,181)(107,180)(108,179)(109,178)(110,177)(111,176)(112,175)(113,174)(114,173)(115,172)(116,171)(117,170)(118,169)(119,168)(120,167)(121,166)(122,165)(123,164)(124,163)(125,162)(126,161)(127,160)(128,159)(129,158)(130,157)(131,156)(132,155)(133,154)(134,153)(135,152)(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)(214,215)(216,284)(217,283)(218,282)(219,281)(220,280)(221,279)(222,278)(223,277)(224,276)(225,275)(226,274)(227,273)(228,272)(229,271)(230,270)(231,269)(232,268)(233,267)(234,266)(235,265)(236,264)(237,263)(238,262)(239,261)(240,260)(241,259)(242,258)(243,257)(244,256)(245,255)(246,254)(247,253)(248,252)(249,251)(285,357)(286,356)(287,426)(288,425)(289,424)(290,423)(291,422)(292,421)(293,420)(294,419)(295,418)(296,417)(297,416)(298,415)(299,414)(300,413)(301,412)(302,411)(303,410)(304,409)(305,408)(306,407)(307,406)(308,405)(309,404)(310,403)(311,402)(312,401)(313,400)(314,399)(315,398)(316,397)(317,396)(318,395)(319,394)(320,393)(321,392)(322,391)(323,390)(324,389)(325,388)(326,387)(327,386)(328,385)(329,384)(330,383)(331,382)(332,381)(333,380)(334,379)(335,378)(336,377)(337,376)(338,375)(339,374)(340,373)(341,372)(342,371)(343,370)(344,369)(345,368)(346,367)(347,366)(348,365)(349,364)(350,363)(351,362)(352,361)(353,360)(354,359)(355,358);;
s2 := (  1,285)(  2,286)(  3,287)(  4,288)(  5,289)(  6,290)(  7,291)(  8,292)(  9,293)( 10,294)( 11,295)( 12,296)( 13,297)( 14,298)( 15,299)( 16,300)( 17,301)( 18,302)( 19,303)( 20,304)( 21,305)( 22,306)( 23,307)( 24,308)( 25,309)( 26,310)( 27,311)( 28,312)( 29,313)( 30,314)( 31,315)( 32,316)( 33,317)( 34,318)( 35,319)( 36,320)( 37,321)( 38,322)( 39,323)( 40,324)( 41,325)( 42,326)( 43,327)( 44,328)( 45,329)( 46,330)( 47,331)( 48,332)( 49,333)( 50,334)( 51,335)( 52,336)( 53,337)( 54,338)( 55,339)( 56,340)( 57,341)( 58,342)( 59,343)( 60,344)( 61,345)( 62,346)( 63,347)( 64,348)( 65,349)( 66,350)( 67,351)( 68,352)( 69,353)( 70,354)( 71,355)( 72,214)( 73,215)( 74,216)( 75,217)( 76,218)( 77,219)( 78,220)( 79,221)( 80,222)( 81,223)( 82,224)( 83,225)( 84,226)( 85,227)( 86,228)( 87,229)( 88,230)( 89,231)( 90,232)( 91,233)( 92,234)( 93,235)( 94,236)( 95,237)( 96,238)( 97,239)( 98,240)( 99,241)(100,242)(101,243)(102,244)(103,245)(104,246)(105,247)(106,248)(107,249)(108,250)(109,251)(110,252)(111,253)(112,254)(113,255)(114,256)(115,257)(116,258)(117,259)(118,260)(119,261)(120,262)(121,263)(122,264)(123,265)(124,266)(125,267)(126,268)(127,269)(128,270)(129,271)(130,272)(131,273)(132,274)(133,275)(134,276)(135,277)(136,278)(137,279)(138,280)(139,281)(140,282)(141,283)(142,284)(143,356)(144,357)(145,358)(146,359)(147,360)(148,361)(149,362)(150,363)(151,364)(152,365)(153,366)(154,367)(155,368)(156,369)(157,370)(158,371)(159,372)(160,373)(161,374)(162,375)(163,376)(164,377)(165,378)(166,379)(167,380)(168,381)(169,382)(170,383)(171,384)(172,385)(173,386)(174,387)(175,388)(176,389)(177,390)(178,391)(179,392)(180,393)(181,394)(182,395)(183,396)(184,397)(185,398)(186,399)(187,400)(188,401)(189,402)(190,403)(191,404)(192,405)(193,406)(194,407)(195,408)(196,409)(197,410)(198,411)(199,412)(200,413)(201,414)(202,415)(203,416)(204,417)(205,418)(206,419)(207,420)(208,421)(209,422)(210,423)(211,424)(212,425)(213,426);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*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*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(426)!(  2, 71)(  3, 70)(  4, 69)(  5, 68)(  6, 67)(  7, 66)(  8, 65)(  9, 64)( 10, 63)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 58)( 16, 57)( 17, 56)( 18, 55)( 19, 54)( 20, 53)( 21, 52)( 22, 51)( 23, 50)( 24, 49)( 25, 48)( 26, 47)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 36, 37)( 73,142)( 74,141)( 75,140)( 76,139)( 77,138)( 78,137)( 79,136)( 80,135)( 81,134)( 82,133)( 83,132)( 84,131)( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)( 91,124)( 92,123)( 93,122)( 94,121)( 95,120)( 96,119)( 97,118)( 98,117)( 99,116)(100,115)(101,114)(102,113)(103,112)(104,111)(105,110)(106,109)(107,108)(144,213)(145,212)(146,211)(147,210)(148,209)(149,208)(150,207)(151,206)(152,205)(153,204)(154,203)(155,202)(156,201)(157,200)(158,199)(159,198)(160,197)(161,196)(162,195)(163,194)(164,193)(165,192)(166,191)(167,190)(168,189)(169,188)(170,187)(171,186)(172,185)(173,184)(174,183)(175,182)(176,181)(177,180)(178,179)(215,284)(216,283)(217,282)(218,281)(219,280)(220,279)(221,278)(222,277)(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)(229,270)(230,269)(231,268)(232,267)(233,266)(234,265)(235,264)(236,263)(237,262)(238,261)(239,260)(240,259)(241,258)(242,257)(243,256)(244,255)(245,254)(246,253)(247,252)(248,251)(249,250)(286,355)(287,354)(288,353)(289,352)(290,351)(291,350)(292,349)(293,348)(294,347)(295,346)(296,345)(297,344)(298,343)(299,342)(300,341)(301,340)(302,339)(303,338)(304,337)(305,336)(306,335)(307,334)(308,333)(309,332)(310,331)(311,330)(312,329)(313,328)(314,327)(315,326)(316,325)(317,324)(318,323)(319,322)(320,321)(357,426)(358,425)(359,424)(360,423)(361,422)(362,421)(363,420)(364,419)(365,418)(366,417)(367,416)(368,415)(369,414)(370,413)(371,412)(372,411)(373,410)(374,409)(375,408)(376,407)(377,406)(378,405)(379,404)(380,403)(381,402)(382,401)(383,400)(384,399)(385,398)(386,397)(387,396)(388,395)(389,394)(390,393)(391,392);
s1 := Sym(426)!(  1,  2)(  3, 71)(  4, 70)(  5, 69)(  6, 68)(  7, 67)(  8, 66)(  9, 65)( 10, 64)( 11, 63)( 12, 62)( 13, 61)( 14, 60)( 15, 59)( 16, 58)( 17, 57)( 18, 56)( 19, 55)( 20, 54)( 21, 53)( 22, 52)( 23, 51)( 24, 50)( 25, 49)( 26, 48)( 27, 47)( 28, 46)( 29, 45)( 30, 44)( 31, 43)( 32, 42)( 33, 41)( 34, 40)( 35, 39)( 36, 38)( 72,144)( 73,143)( 74,213)( 75,212)( 76,211)( 77,210)( 78,209)( 79,208)( 80,207)( 81,206)( 82,205)( 83,204)( 84,203)( 85,202)( 86,201)( 87,200)( 88,199)( 89,198)( 90,197)( 91,196)( 92,195)( 93,194)( 94,193)( 95,192)( 96,191)( 97,190)( 98,189)( 99,188)(100,187)(101,186)(102,185)(103,184)(104,183)(105,182)(106,181)(107,180)(108,179)(109,178)(110,177)(111,176)(112,175)(113,174)(114,173)(115,172)(116,171)(117,170)(118,169)(119,168)(120,167)(121,166)(122,165)(123,164)(124,163)(125,162)(126,161)(127,160)(128,159)(129,158)(130,157)(131,156)(132,155)(133,154)(134,153)(135,152)(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)(214,215)(216,284)(217,283)(218,282)(219,281)(220,280)(221,279)(222,278)(223,277)(224,276)(225,275)(226,274)(227,273)(228,272)(229,271)(230,270)(231,269)(232,268)(233,267)(234,266)(235,265)(236,264)(237,263)(238,262)(239,261)(240,260)(241,259)(242,258)(243,257)(244,256)(245,255)(246,254)(247,253)(248,252)(249,251)(285,357)(286,356)(287,426)(288,425)(289,424)(290,423)(291,422)(292,421)(293,420)(294,419)(295,418)(296,417)(297,416)(298,415)(299,414)(300,413)(301,412)(302,411)(303,410)(304,409)(305,408)(306,407)(307,406)(308,405)(309,404)(310,403)(311,402)(312,401)(313,400)(314,399)(315,398)(316,397)(317,396)(318,395)(319,394)(320,393)(321,392)(322,391)(323,390)(324,389)(325,388)(326,387)(327,386)(328,385)(329,384)(330,383)(331,382)(332,381)(333,380)(334,379)(335,378)(336,377)(337,376)(338,375)(339,374)(340,373)(341,372)(342,371)(343,370)(344,369)(345,368)(346,367)(347,366)(348,365)(349,364)(350,363)(351,362)(352,361)(353,360)(354,359)(355,358);
s2 := Sym(426)!(  1,285)(  2,286)(  3,287)(  4,288)(  5,289)(  6,290)(  7,291)(  8,292)(  9,293)( 10,294)( 11,295)( 12,296)( 13,297)( 14,298)( 15,299)( 16,300)( 17,301)( 18,302)( 19,303)( 20,304)( 21,305)( 22,306)( 23,307)( 24,308)( 25,309)( 26,310)( 27,311)( 28,312)( 29,313)( 30,314)( 31,315)( 32,316)( 33,317)( 34,318)( 35,319)( 36,320)( 37,321)( 38,322)( 39,323)( 40,324)( 41,325)( 42,326)( 43,327)( 44,328)( 45,329)( 46,330)( 47,331)( 48,332)( 49,333)( 50,334)( 51,335)( 52,336)( 53,337)( 54,338)( 55,339)( 56,340)( 57,341)( 58,342)( 59,343)( 60,344)( 61,345)( 62,346)( 63,347)( 64,348)( 65,349)( 66,350)( 67,351)( 68,352)( 69,353)( 70,354)( 71,355)( 72,214)( 73,215)( 74,216)( 75,217)( 76,218)( 77,219)( 78,220)( 79,221)( 80,222)( 81,223)( 82,224)( 83,225)( 84,226)( 85,227)( 86,228)( 87,229)( 88,230)( 89,231)( 90,232)( 91,233)( 92,234)( 93,235)( 94,236)( 95,237)( 96,238)( 97,239)( 98,240)( 99,241)(100,242)(101,243)(102,244)(103,245)(104,246)(105,247)(106,248)(107,249)(108,250)(109,251)(110,252)(111,253)(112,254)(113,255)(114,256)(115,257)(116,258)(117,259)(118,260)(119,261)(120,262)(121,263)(122,264)(123,265)(124,266)(125,267)(126,268)(127,269)(128,270)(129,271)(130,272)(131,273)(132,274)(133,275)(134,276)(135,277)(136,278)(137,279)(138,280)(139,281)(140,282)(141,283)(142,284)(143,356)(144,357)(145,358)(146,359)(147,360)(148,361)(149,362)(150,363)(151,364)(152,365)(153,366)(154,367)(155,368)(156,369)(157,370)(158,371)(159,372)(160,373)(161,374)(162,375)(163,376)(164,377)(165,378)(166,379)(167,380)(168,381)(169,382)(170,383)(171,384)(172,385)(173,386)(174,387)(175,388)(176,389)(177,390)(178,391)(179,392)(180,393)(181,394)(182,395)(183,396)(184,397)(185,398)(186,399)(187,400)(188,401)(189,402)(190,403)(191,404)(192,405)(193,406)(194,407)(195,408)(196,409)(197,410)(198,411)(199,412)(200,413)(201,414)(202,415)(203,416)(204,417)(205,418)(206,419)(207,420)(208,421)(209,422)(210,423)(211,424)(212,425)(213,426);
poly := sub<Sym(426)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*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*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