Polytope of Type {190,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {190,4}*1520
Also Known As : {190,4|2}. if this polytope has another name.
Group : SmallGroup(1520,160)
Rank : 3
Schlafli Type : {190,4}
Number of vertices, edges, etc : 190, 380, 4
Order of s0s1s2 : 380
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) :
   2-fold quotients : {190,2}*760
   4-fold quotients : {95,2}*380
   5-fold quotients : {38,4}*304
   10-fold quotients : {38,2}*152
   19-fold quotients : {10,4}*80
   20-fold quotients : {19,2}*76
   38-fold quotients : {10,2}*40
   76-fold quotients : {5,2}*20
   95-fold quotients : {2,4}*16
   190-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, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)( 10, 11)( 20, 77)( 21, 95)( 22, 94)( 23, 93)( 24, 92)( 25, 91)( 26, 90)( 27, 89)( 28, 88)( 29, 87)( 30, 86)( 31, 85)( 32, 84)( 33, 83)( 34, 82)( 35, 81)( 36, 80)( 37, 79)( 38, 78)( 39, 58)( 40, 76)( 41, 75)( 42, 74)( 43, 73)( 44, 72)( 45, 71)( 46, 70)( 47, 69)( 48, 68)( 49, 67)( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(115,172)(116,190)(117,189)(118,188)(119,187)(120,186)(121,185)(122,184)(123,183)(124,182)(125,181)(126,180)(127,179)(128,178)(129,177)(130,176)(131,175)(132,174)(133,173)(134,153)(135,171)(136,170)(137,169)(138,168)(139,167)(140,166)(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)(147,159)(148,158)(149,157)(150,156)(151,155)(152,154)(192,209)(193,208)(194,207)(195,206)(196,205)(197,204)(198,203)(199,202)(200,201)(210,267)(211,285)(212,284)(213,283)(214,282)(215,281)(216,280)(217,279)(218,278)(219,277)(220,276)(221,275)(222,274)(223,273)(224,272)(225,271)(226,270)(227,269)(228,268)(229,248)(230,266)(231,265)(232,264)(233,263)(234,262)(235,261)(236,260)(237,259)(238,258)(239,257)(240,256)(241,255)(242,254)(243,253)(244,252)(245,251)(246,250)(247,249)(287,304)(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)(305,362)(306,380)(307,379)(308,378)(309,377)(310,376)(311,375)(312,374)(313,373)(314,372)(315,371)(316,370)(317,369)(318,368)(319,367)(320,366)(321,365)(322,364)(323,363)(324,343)(325,361)(326,360)(327,359)(328,358)(329,357)(330,356)(331,355)(332,354)(333,353)(334,352)(335,351)(336,350)(337,349)(338,348)(339,347)(340,346)(341,345)(342,344);;
s1 := (  1, 21)(  2, 20)(  3, 38)(  4, 37)(  5, 36)(  6, 35)(  7, 34)(  8, 33)(  9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 39, 78)( 40, 77)( 41, 95)( 42, 94)( 43, 93)( 44, 92)( 45, 91)( 46, 90)( 47, 89)( 48, 88)( 49, 87)( 50, 86)( 51, 85)( 52, 84)( 53, 83)( 54, 82)( 55, 81)( 56, 80)( 57, 79)( 58, 59)( 60, 76)( 61, 75)( 62, 74)( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 96,116)( 97,115)( 98,133)( 99,132)(100,131)(101,130)(102,129)(103,128)(104,127)(105,126)(106,125)(107,124)(108,123)(109,122)(110,121)(111,120)(112,119)(113,118)(114,117)(134,173)(135,172)(136,190)(137,189)(138,188)(139,187)(140,186)(141,185)(142,184)(143,183)(144,182)(145,181)(146,180)(147,179)(148,178)(149,177)(150,176)(151,175)(152,174)(153,154)(155,171)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)(162,164)(191,306)(192,305)(193,323)(194,322)(195,321)(196,320)(197,319)(198,318)(199,317)(200,316)(201,315)(202,314)(203,313)(204,312)(205,311)(206,310)(207,309)(208,308)(209,307)(210,287)(211,286)(212,304)(213,303)(214,302)(215,301)(216,300)(217,299)(218,298)(219,297)(220,296)(221,295)(222,294)(223,293)(224,292)(225,291)(226,290)(227,289)(228,288)(229,363)(230,362)(231,380)(232,379)(233,378)(234,377)(235,376)(236,375)(237,374)(238,373)(239,372)(240,371)(241,370)(242,369)(243,368)(244,367)(245,366)(246,365)(247,364)(248,344)(249,343)(250,361)(251,360)(252,359)(253,358)(254,357)(255,356)(256,355)(257,354)(258,353)(259,352)(260,351)(261,350)(262,349)(263,348)(264,347)(265,346)(266,345)(267,325)(268,324)(269,342)(270,341)(271,340)(272,339)(273,338)(274,337)(275,336)(276,335)(277,334)(278,333)(279,332)(280,331)(281,330)(282,329)(283,328)(284,327)(285,326);;
s2 := (  1,191)(  2,192)(  3,193)(  4,194)(  5,195)(  6,196)(  7,197)(  8,198)(  9,199)( 10,200)( 11,201)( 12,202)( 13,203)( 14,204)( 15,205)( 16,206)( 17,207)( 18,208)( 19,209)( 20,210)( 21,211)( 22,212)( 23,213)( 24,214)( 25,215)( 26,216)( 27,217)( 28,218)( 29,219)( 30,220)( 31,221)( 32,222)( 33,223)( 34,224)( 35,225)( 36,226)( 37,227)( 38,228)( 39,229)( 40,230)( 41,231)( 42,232)( 43,233)( 44,234)( 45,235)( 46,236)( 47,237)( 48,238)( 49,239)( 50,240)( 51,241)( 52,242)( 53,243)( 54,244)( 55,245)( 56,246)( 57,247)( 58,248)( 59,249)( 60,250)( 61,251)( 62,252)( 63,253)( 64,254)( 65,255)( 66,256)( 67,257)( 68,258)( 69,259)( 70,260)( 71,261)( 72,262)( 73,263)( 74,264)( 75,265)( 76,266)( 77,267)( 78,268)( 79,269)( 80,270)( 81,271)( 82,272)( 83,273)( 84,274)( 85,275)( 86,276)( 87,277)( 88,278)( 89,279)( 90,280)( 91,281)( 92,282)( 93,283)( 94,284)( 95,285)( 96,286)( 97,287)( 98,288)( 99,289)(100,290)(101,291)(102,292)(103,293)(104,294)(105,295)(106,296)(107,297)(108,298)(109,299)(110,300)(111,301)(112,302)(113,303)(114,304)(115,305)(116,306)(117,307)(118,308)(119,309)(120,310)(121,311)(122,312)(123,313)(124,314)(125,315)(126,316)(127,317)(128,318)(129,319)(130,320)(131,321)(132,322)(133,323)(134,324)(135,325)(136,326)(137,327)(138,328)(139,329)(140,330)(141,331)(142,332)(143,333)(144,334)(145,335)(146,336)(147,337)(148,338)(149,339)(150,340)(151,341)(152,342)(153,343)(154,344)(155,345)(156,346)(157,347)(158,348)(159,349)(160,350)(161,351)(162,352)(163,353)(164,354)(165,355)(166,356)(167,357)(168,358)(169,359)(170,360)(171,361)(172,362)(173,363)(174,364)(175,365)(176,366)(177,367)(178,368)(179,369)(180,370)(181,371)(182,372)(183,373)(184,374)(185,375)(186,376)(187,377)(188,378)(189,379)(190,380);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(380)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)( 10, 11)( 20, 77)( 21, 95)( 22, 94)( 23, 93)( 24, 92)( 25, 91)( 26, 90)( 27, 89)( 28, 88)( 29, 87)( 30, 86)( 31, 85)( 32, 84)( 33, 83)( 34, 82)( 35, 81)( 36, 80)( 37, 79)( 38, 78)( 39, 58)( 40, 76)( 41, 75)( 42, 74)( 43, 73)( 44, 72)( 45, 71)( 46, 70)( 47, 69)( 48, 68)( 49, 67)( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(115,172)(116,190)(117,189)(118,188)(119,187)(120,186)(121,185)(122,184)(123,183)(124,182)(125,181)(126,180)(127,179)(128,178)(129,177)(130,176)(131,175)(132,174)(133,173)(134,153)(135,171)(136,170)(137,169)(138,168)(139,167)(140,166)(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)(147,159)(148,158)(149,157)(150,156)(151,155)(152,154)(192,209)(193,208)(194,207)(195,206)(196,205)(197,204)(198,203)(199,202)(200,201)(210,267)(211,285)(212,284)(213,283)(214,282)(215,281)(216,280)(217,279)(218,278)(219,277)(220,276)(221,275)(222,274)(223,273)(224,272)(225,271)(226,270)(227,269)(228,268)(229,248)(230,266)(231,265)(232,264)(233,263)(234,262)(235,261)(236,260)(237,259)(238,258)(239,257)(240,256)(241,255)(242,254)(243,253)(244,252)(245,251)(246,250)(247,249)(287,304)(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)(305,362)(306,380)(307,379)(308,378)(309,377)(310,376)(311,375)(312,374)(313,373)(314,372)(315,371)(316,370)(317,369)(318,368)(319,367)(320,366)(321,365)(322,364)(323,363)(324,343)(325,361)(326,360)(327,359)(328,358)(329,357)(330,356)(331,355)(332,354)(333,353)(334,352)(335,351)(336,350)(337,349)(338,348)(339,347)(340,346)(341,345)(342,344);
s1 := Sym(380)!(  1, 21)(  2, 20)(  3, 38)(  4, 37)(  5, 36)(  6, 35)(  7, 34)(  8, 33)(  9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 39, 78)( 40, 77)( 41, 95)( 42, 94)( 43, 93)( 44, 92)( 45, 91)( 46, 90)( 47, 89)( 48, 88)( 49, 87)( 50, 86)( 51, 85)( 52, 84)( 53, 83)( 54, 82)( 55, 81)( 56, 80)( 57, 79)( 58, 59)( 60, 76)( 61, 75)( 62, 74)( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 96,116)( 97,115)( 98,133)( 99,132)(100,131)(101,130)(102,129)(103,128)(104,127)(105,126)(106,125)(107,124)(108,123)(109,122)(110,121)(111,120)(112,119)(113,118)(114,117)(134,173)(135,172)(136,190)(137,189)(138,188)(139,187)(140,186)(141,185)(142,184)(143,183)(144,182)(145,181)(146,180)(147,179)(148,178)(149,177)(150,176)(151,175)(152,174)(153,154)(155,171)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)(162,164)(191,306)(192,305)(193,323)(194,322)(195,321)(196,320)(197,319)(198,318)(199,317)(200,316)(201,315)(202,314)(203,313)(204,312)(205,311)(206,310)(207,309)(208,308)(209,307)(210,287)(211,286)(212,304)(213,303)(214,302)(215,301)(216,300)(217,299)(218,298)(219,297)(220,296)(221,295)(222,294)(223,293)(224,292)(225,291)(226,290)(227,289)(228,288)(229,363)(230,362)(231,380)(232,379)(233,378)(234,377)(235,376)(236,375)(237,374)(238,373)(239,372)(240,371)(241,370)(242,369)(243,368)(244,367)(245,366)(246,365)(247,364)(248,344)(249,343)(250,361)(251,360)(252,359)(253,358)(254,357)(255,356)(256,355)(257,354)(258,353)(259,352)(260,351)(261,350)(262,349)(263,348)(264,347)(265,346)(266,345)(267,325)(268,324)(269,342)(270,341)(271,340)(272,339)(273,338)(274,337)(275,336)(276,335)(277,334)(278,333)(279,332)(280,331)(281,330)(282,329)(283,328)(284,327)(285,326);
s2 := Sym(380)!(  1,191)(  2,192)(  3,193)(  4,194)(  5,195)(  6,196)(  7,197)(  8,198)(  9,199)( 10,200)( 11,201)( 12,202)( 13,203)( 14,204)( 15,205)( 16,206)( 17,207)( 18,208)( 19,209)( 20,210)( 21,211)( 22,212)( 23,213)( 24,214)( 25,215)( 26,216)( 27,217)( 28,218)( 29,219)( 30,220)( 31,221)( 32,222)( 33,223)( 34,224)( 35,225)( 36,226)( 37,227)( 38,228)( 39,229)( 40,230)( 41,231)( 42,232)( 43,233)( 44,234)( 45,235)( 46,236)( 47,237)( 48,238)( 49,239)( 50,240)( 51,241)( 52,242)( 53,243)( 54,244)( 55,245)( 56,246)( 57,247)( 58,248)( 59,249)( 60,250)( 61,251)( 62,252)( 63,253)( 64,254)( 65,255)( 66,256)( 67,257)( 68,258)( 69,259)( 70,260)( 71,261)( 72,262)( 73,263)( 74,264)( 75,265)( 76,266)( 77,267)( 78,268)( 79,269)( 80,270)( 81,271)( 82,272)( 83,273)( 84,274)( 85,275)( 86,276)( 87,277)( 88,278)( 89,279)( 90,280)( 91,281)( 92,282)( 93,283)( 94,284)( 95,285)( 96,286)( 97,287)( 98,288)( 99,289)(100,290)(101,291)(102,292)(103,293)(104,294)(105,295)(106,296)(107,297)(108,298)(109,299)(110,300)(111,301)(112,302)(113,303)(114,304)(115,305)(116,306)(117,307)(118,308)(119,309)(120,310)(121,311)(122,312)(123,313)(124,314)(125,315)(126,316)(127,317)(128,318)(129,319)(130,320)(131,321)(132,322)(133,323)(134,324)(135,325)(136,326)(137,327)(138,328)(139,329)(140,330)(141,331)(142,332)(143,333)(144,334)(145,335)(146,336)(147,337)(148,338)(149,339)(150,340)(151,341)(152,342)(153,343)(154,344)(155,345)(156,346)(157,347)(158,348)(159,349)(160,350)(161,351)(162,352)(163,353)(164,354)(165,355)(166,356)(167,357)(168,358)(169,359)(170,360)(171,361)(172,362)(173,363)(174,364)(175,365)(176,366)(177,367)(178,368)(179,369)(180,370)(181,371)(182,372)(183,373)(184,374)(185,375)(186,376)(187,377)(188,378)(189,379)(190,380);
poly := sub<Sym(380)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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