Polytope of Type {182,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {182,4}*1456
Also Known As : {182,4|2}. if this polytope has another name.
Group : SmallGroup(1456,160)
Rank : 3
Schlafli Type : {182,4}
Number of vertices, edges, etc : 182, 364, 4
Order of s0s1s2 : 364
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 : {182,2}*728
   4-fold quotients : {91,2}*364
   7-fold quotients : {26,4}*208
   13-fold quotients : {14,4}*112
   14-fold quotients : {26,2}*104
   26-fold quotients : {14,2}*56
   28-fold quotients : {13,2}*52
   52-fold quotients : {7,2}*28
   91-fold quotients : {2,4}*16
   182-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, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 14, 79)( 15, 91)( 16, 90)( 17, 89)( 18, 88)( 19, 87)( 20, 86)( 21, 85)( 22, 84)( 23, 83)( 24, 82)( 25, 81)( 26, 80)( 27, 66)( 28, 78)( 29, 77)( 30, 76)( 31, 75)( 32, 74)( 33, 73)( 34, 72)( 35, 71)( 36, 70)( 37, 69)( 38, 68)( 39, 67)( 40, 53)( 41, 65)( 42, 64)( 43, 63)( 44, 62)( 45, 61)( 46, 60)( 47, 59)( 48, 58)( 49, 57)( 50, 56)( 51, 55)( 52, 54)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)(105,170)(106,182)(107,181)(108,180)(109,179)(110,178)(111,177)(112,176)(113,175)(114,174)(115,173)(116,172)(117,171)(118,157)(119,169)(120,168)(121,167)(122,166)(123,165)(124,164)(125,163)(126,162)(127,161)(128,160)(129,159)(130,158)(131,144)(132,156)(133,155)(134,154)(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)(142,146)(143,145)(184,195)(185,194)(186,193)(187,192)(188,191)(189,190)(196,261)(197,273)(198,272)(199,271)(200,270)(201,269)(202,268)(203,267)(204,266)(205,265)(206,264)(207,263)(208,262)(209,248)(210,260)(211,259)(212,258)(213,257)(214,256)(215,255)(216,254)(217,253)(218,252)(219,251)(220,250)(221,249)(222,235)(223,247)(224,246)(225,245)(226,244)(227,243)(228,242)(229,241)(230,240)(231,239)(232,238)(233,237)(234,236)(275,286)(276,285)(277,284)(278,283)(279,282)(280,281)(287,352)(288,364)(289,363)(290,362)(291,361)(292,360)(293,359)(294,358)(295,357)(296,356)(297,355)(298,354)(299,353)(300,339)(301,351)(302,350)(303,349)(304,348)(305,347)(306,346)(307,345)(308,344)(309,343)(310,342)(311,341)(312,340)(313,326)(314,338)(315,337)(316,336)(317,335)(318,334)(319,333)(320,332)(321,331)(322,330)(323,329)(324,328)(325,327);;
s1 := (  1, 15)(  2, 14)(  3, 26)(  4, 25)(  5, 24)(  6, 23)(  7, 22)(  8, 21)(  9, 20)( 10, 19)( 11, 18)( 12, 17)( 13, 16)( 27, 80)( 28, 79)( 29, 91)( 30, 90)( 31, 89)( 32, 88)( 33, 87)( 34, 86)( 35, 85)( 36, 84)( 37, 83)( 38, 82)( 39, 81)( 40, 67)( 41, 66)( 42, 78)( 43, 77)( 44, 76)( 45, 75)( 46, 74)( 47, 73)( 48, 72)( 49, 71)( 50, 70)( 51, 69)( 52, 68)( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 92,106)( 93,105)( 94,117)( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(118,171)(119,170)(120,182)(121,181)(122,180)(123,179)(124,178)(125,177)(126,176)(127,175)(128,174)(129,173)(130,172)(131,158)(132,157)(133,169)(134,168)(135,167)(136,166)(137,165)(138,164)(139,163)(140,162)(141,161)(142,160)(143,159)(144,145)(146,156)(147,155)(148,154)(149,153)(150,152)(183,288)(184,287)(185,299)(186,298)(187,297)(188,296)(189,295)(190,294)(191,293)(192,292)(193,291)(194,290)(195,289)(196,275)(197,274)(198,286)(199,285)(200,284)(201,283)(202,282)(203,281)(204,280)(205,279)(206,278)(207,277)(208,276)(209,353)(210,352)(211,364)(212,363)(213,362)(214,361)(215,360)(216,359)(217,358)(218,357)(219,356)(220,355)(221,354)(222,340)(223,339)(224,351)(225,350)(226,349)(227,348)(228,347)(229,346)(230,345)(231,344)(232,343)(233,342)(234,341)(235,327)(236,326)(237,338)(238,337)(239,336)(240,335)(241,334)(242,333)(243,332)(244,331)(245,330)(246,329)(247,328)(248,314)(249,313)(250,325)(251,324)(252,323)(253,322)(254,321)(255,320)(256,319)(257,318)(258,317)(259,316)(260,315)(261,301)(262,300)(263,312)(264,311)(265,310)(266,309)(267,308)(268,307)(269,306)(270,305)(271,304)(272,303)(273,302);;
s2 := (  1,183)(  2,184)(  3,185)(  4,186)(  5,187)(  6,188)(  7,189)(  8,190)(  9,191)( 10,192)( 11,193)( 12,194)( 13,195)( 14,196)( 15,197)( 16,198)( 17,199)( 18,200)( 19,201)( 20,202)( 21,203)( 22,204)( 23,205)( 24,206)( 25,207)( 26,208)( 27,209)( 28,210)( 29,211)( 30,212)( 31,213)( 32,214)( 33,215)( 34,216)( 35,217)( 36,218)( 37,219)( 38,220)( 39,221)( 40,222)( 41,223)( 42,224)( 43,225)( 44,226)( 45,227)( 46,228)( 47,229)( 48,230)( 49,231)( 50,232)( 51,233)( 52,234)( 53,235)( 54,236)( 55,237)( 56,238)( 57,239)( 58,240)( 59,241)( 60,242)( 61,243)( 62,244)( 63,245)( 64,246)( 65,247)( 66,248)( 67,249)( 68,250)( 69,251)( 70,252)( 71,253)( 72,254)( 73,255)( 74,256)( 75,257)( 76,258)( 77,259)( 78,260)( 79,261)( 80,262)( 81,263)( 82,264)( 83,265)( 84,266)( 85,267)( 86,268)( 87,269)( 88,270)( 89,271)( 90,272)( 91,273)( 92,274)( 93,275)( 94,276)( 95,277)( 96,278)( 97,279)( 98,280)( 99,281)(100,282)(101,283)(102,284)(103,285)(104,286)(105,287)(106,288)(107,289)(108,290)(109,291)(110,292)(111,293)(112,294)(113,295)(114,296)(115,297)(116,298)(117,299)(118,300)(119,301)(120,302)(121,303)(122,304)(123,305)(124,306)(125,307)(126,308)(127,309)(128,310)(129,311)(130,312)(131,313)(132,314)(133,315)(134,316)(135,317)(136,318)(137,319)(138,320)(139,321)(140,322)(141,323)(142,324)(143,325)(144,326)(145,327)(146,328)(147,329)(148,330)(149,331)(150,332)(151,333)(152,334)(153,335)(154,336)(155,337)(156,338)(157,339)(158,340)(159,341)(160,342)(161,343)(162,344)(163,345)(164,346)(165,347)(166,348)(167,349)(168,350)(169,351)(170,352)(171,353)(172,354)(173,355)(174,356)(175,357)(176,358)(177,359)(178,360)(179,361)(180,362)(181,363)(182,364);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(364)!(  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 14, 79)( 15, 91)( 16, 90)( 17, 89)( 18, 88)( 19, 87)( 20, 86)( 21, 85)( 22, 84)( 23, 83)( 24, 82)( 25, 81)( 26, 80)( 27, 66)( 28, 78)( 29, 77)( 30, 76)( 31, 75)( 32, 74)( 33, 73)( 34, 72)( 35, 71)( 36, 70)( 37, 69)( 38, 68)( 39, 67)( 40, 53)( 41, 65)( 42, 64)( 43, 63)( 44, 62)( 45, 61)( 46, 60)( 47, 59)( 48, 58)( 49, 57)( 50, 56)( 51, 55)( 52, 54)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)(105,170)(106,182)(107,181)(108,180)(109,179)(110,178)(111,177)(112,176)(113,175)(114,174)(115,173)(116,172)(117,171)(118,157)(119,169)(120,168)(121,167)(122,166)(123,165)(124,164)(125,163)(126,162)(127,161)(128,160)(129,159)(130,158)(131,144)(132,156)(133,155)(134,154)(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)(142,146)(143,145)(184,195)(185,194)(186,193)(187,192)(188,191)(189,190)(196,261)(197,273)(198,272)(199,271)(200,270)(201,269)(202,268)(203,267)(204,266)(205,265)(206,264)(207,263)(208,262)(209,248)(210,260)(211,259)(212,258)(213,257)(214,256)(215,255)(216,254)(217,253)(218,252)(219,251)(220,250)(221,249)(222,235)(223,247)(224,246)(225,245)(226,244)(227,243)(228,242)(229,241)(230,240)(231,239)(232,238)(233,237)(234,236)(275,286)(276,285)(277,284)(278,283)(279,282)(280,281)(287,352)(288,364)(289,363)(290,362)(291,361)(292,360)(293,359)(294,358)(295,357)(296,356)(297,355)(298,354)(299,353)(300,339)(301,351)(302,350)(303,349)(304,348)(305,347)(306,346)(307,345)(308,344)(309,343)(310,342)(311,341)(312,340)(313,326)(314,338)(315,337)(316,336)(317,335)(318,334)(319,333)(320,332)(321,331)(322,330)(323,329)(324,328)(325,327);
s1 := Sym(364)!(  1, 15)(  2, 14)(  3, 26)(  4, 25)(  5, 24)(  6, 23)(  7, 22)(  8, 21)(  9, 20)( 10, 19)( 11, 18)( 12, 17)( 13, 16)( 27, 80)( 28, 79)( 29, 91)( 30, 90)( 31, 89)( 32, 88)( 33, 87)( 34, 86)( 35, 85)( 36, 84)( 37, 83)( 38, 82)( 39, 81)( 40, 67)( 41, 66)( 42, 78)( 43, 77)( 44, 76)( 45, 75)( 46, 74)( 47, 73)( 48, 72)( 49, 71)( 50, 70)( 51, 69)( 52, 68)( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 92,106)( 93,105)( 94,117)( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(118,171)(119,170)(120,182)(121,181)(122,180)(123,179)(124,178)(125,177)(126,176)(127,175)(128,174)(129,173)(130,172)(131,158)(132,157)(133,169)(134,168)(135,167)(136,166)(137,165)(138,164)(139,163)(140,162)(141,161)(142,160)(143,159)(144,145)(146,156)(147,155)(148,154)(149,153)(150,152)(183,288)(184,287)(185,299)(186,298)(187,297)(188,296)(189,295)(190,294)(191,293)(192,292)(193,291)(194,290)(195,289)(196,275)(197,274)(198,286)(199,285)(200,284)(201,283)(202,282)(203,281)(204,280)(205,279)(206,278)(207,277)(208,276)(209,353)(210,352)(211,364)(212,363)(213,362)(214,361)(215,360)(216,359)(217,358)(218,357)(219,356)(220,355)(221,354)(222,340)(223,339)(224,351)(225,350)(226,349)(227,348)(228,347)(229,346)(230,345)(231,344)(232,343)(233,342)(234,341)(235,327)(236,326)(237,338)(238,337)(239,336)(240,335)(241,334)(242,333)(243,332)(244,331)(245,330)(246,329)(247,328)(248,314)(249,313)(250,325)(251,324)(252,323)(253,322)(254,321)(255,320)(256,319)(257,318)(258,317)(259,316)(260,315)(261,301)(262,300)(263,312)(264,311)(265,310)(266,309)(267,308)(268,307)(269,306)(270,305)(271,304)(272,303)(273,302);
s2 := Sym(364)!(  1,183)(  2,184)(  3,185)(  4,186)(  5,187)(  6,188)(  7,189)(  8,190)(  9,191)( 10,192)( 11,193)( 12,194)( 13,195)( 14,196)( 15,197)( 16,198)( 17,199)( 18,200)( 19,201)( 20,202)( 21,203)( 22,204)( 23,205)( 24,206)( 25,207)( 26,208)( 27,209)( 28,210)( 29,211)( 30,212)( 31,213)( 32,214)( 33,215)( 34,216)( 35,217)( 36,218)( 37,219)( 38,220)( 39,221)( 40,222)( 41,223)( 42,224)( 43,225)( 44,226)( 45,227)( 46,228)( 47,229)( 48,230)( 49,231)( 50,232)( 51,233)( 52,234)( 53,235)( 54,236)( 55,237)( 56,238)( 57,239)( 58,240)( 59,241)( 60,242)( 61,243)( 62,244)( 63,245)( 64,246)( 65,247)( 66,248)( 67,249)( 68,250)( 69,251)( 70,252)( 71,253)( 72,254)( 73,255)( 74,256)( 75,257)( 76,258)( 77,259)( 78,260)( 79,261)( 80,262)( 81,263)( 82,264)( 83,265)( 84,266)( 85,267)( 86,268)( 87,269)( 88,270)( 89,271)( 90,272)( 91,273)( 92,274)( 93,275)( 94,276)( 95,277)( 96,278)( 97,279)( 98,280)( 99,281)(100,282)(101,283)(102,284)(103,285)(104,286)(105,287)(106,288)(107,289)(108,290)(109,291)(110,292)(111,293)(112,294)(113,295)(114,296)(115,297)(116,298)(117,299)(118,300)(119,301)(120,302)(121,303)(122,304)(123,305)(124,306)(125,307)(126,308)(127,309)(128,310)(129,311)(130,312)(131,313)(132,314)(133,315)(134,316)(135,317)(136,318)(137,319)(138,320)(139,321)(140,322)(141,323)(142,324)(143,325)(144,326)(145,327)(146,328)(147,329)(148,330)(149,331)(150,332)(151,333)(152,334)(153,335)(154,336)(155,337)(156,338)(157,339)(158,340)(159,341)(160,342)(161,343)(162,344)(163,345)(164,346)(165,347)(166,348)(167,349)(168,350)(169,351)(170,352)(171,353)(172,354)(173,355)(174,356)(175,357)(176,358)(177,359)(178,360)(179,361)(180,362)(181,363)(182,364);
poly := sub<Sym(364)|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 >;
References : None.
to this polytope

Twisty Puzzle