Polytope of Type {20,36}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,36}*1440
Also Known As : {20,36|2}. if this polytope has another name.
Group : SmallGroup(1440,552)
Rank : 3
Schlafli Type : {20,36}
Number of vertices, edges, etc : 20, 360, 36
Order of s0s1s2 : 180
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 : {10,36}*720, {20,18}*720a
   3-fold quotients : {20,12}*480
   4-fold quotients : {10,18}*360
   5-fold quotients : {4,36}*288a
   6-fold quotients : {10,12}*240, {20,6}*240a
   9-fold quotients : {20,4}*160
   10-fold quotients : {2,36}*144, {4,18}*144a
   12-fold quotients : {10,6}*120
   15-fold quotients : {4,12}*96a
   18-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {2,18}*72
   30-fold quotients : {2,12}*48, {4,6}*48a
   36-fold quotients : {10,2}*40
   40-fold quotients : {2,9}*36
   45-fold quotients : {4,4}*32
   60-fold quotients : {2,6}*24
   72-fold quotients : {5,2}*20
   90-fold quotients : {2,4}*16, {4,2}*16
   120-fold quotients : {2,3}*12
   180-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 := (  4, 13)(  5, 14)(  6, 15)(  7, 10)(  8, 11)(  9, 12)( 19, 28)( 20, 29)( 21, 30)( 22, 25)( 23, 26)( 24, 27)( 34, 43)( 35, 44)( 36, 45)( 37, 40)( 38, 41)( 39, 42)( 49, 58)( 50, 59)( 51, 60)( 52, 55)( 53, 56)( 54, 57)( 64, 73)( 65, 74)( 66, 75)( 67, 70)( 68, 71)( 69, 72)( 79, 88)( 80, 89)( 81, 90)( 82, 85)( 83, 86)( 84, 87)( 94,103)( 95,104)( 96,105)( 97,100)( 98,101)( 99,102)(109,118)(110,119)(111,120)(112,115)(113,116)(114,117)(124,133)(125,134)(126,135)(127,130)(128,131)(129,132)(139,148)(140,149)(141,150)(142,145)(143,146)(144,147)(154,163)(155,164)(156,165)(157,160)(158,161)(159,162)(169,178)(170,179)(171,180)(172,175)(173,176)(174,177)(181,226)(182,227)(183,228)(184,238)(185,239)(186,240)(187,235)(188,236)(189,237)(190,232)(191,233)(192,234)(193,229)(194,230)(195,231)(196,241)(197,242)(198,243)(199,253)(200,254)(201,255)(202,250)(203,251)(204,252)(205,247)(206,248)(207,249)(208,244)(209,245)(210,246)(211,256)(212,257)(213,258)(214,268)(215,269)(216,270)(217,265)(218,266)(219,267)(220,262)(221,263)(222,264)(223,259)(224,260)(225,261)(271,316)(272,317)(273,318)(274,328)(275,329)(276,330)(277,325)(278,326)(279,327)(280,322)(281,323)(282,324)(283,319)(284,320)(285,321)(286,331)(287,332)(288,333)(289,343)(290,344)(291,345)(292,340)(293,341)(294,342)(295,337)(296,338)(297,339)(298,334)(299,335)(300,336)(301,346)(302,347)(303,348)(304,358)(305,359)(306,360)(307,355)(308,356)(309,357)(310,352)(311,353)(312,354)(313,349)(314,350)(315,351);;
s1 := (  1,184)(  2,186)(  3,185)(  4,181)(  5,183)(  6,182)(  7,193)(  8,195)(  9,194)( 10,190)( 11,192)( 12,191)( 13,187)( 14,189)( 15,188)( 16,216)( 17,215)( 18,214)( 19,213)( 20,212)( 21,211)( 22,225)( 23,224)( 24,223)( 25,222)( 26,221)( 27,220)( 28,219)( 29,218)( 30,217)( 31,201)( 32,200)( 33,199)( 34,198)( 35,197)( 36,196)( 37,210)( 38,209)( 39,208)( 40,207)( 41,206)( 42,205)( 43,204)( 44,203)( 45,202)( 46,229)( 47,231)( 48,230)( 49,226)( 50,228)( 51,227)( 52,238)( 53,240)( 54,239)( 55,235)( 56,237)( 57,236)( 58,232)( 59,234)( 60,233)( 61,261)( 62,260)( 63,259)( 64,258)( 65,257)( 66,256)( 67,270)( 68,269)( 69,268)( 70,267)( 71,266)( 72,265)( 73,264)( 74,263)( 75,262)( 76,246)( 77,245)( 78,244)( 79,243)( 80,242)( 81,241)( 82,255)( 83,254)( 84,253)( 85,252)( 86,251)( 87,250)( 88,249)( 89,248)( 90,247)( 91,274)( 92,276)( 93,275)( 94,271)( 95,273)( 96,272)( 97,283)( 98,285)( 99,284)(100,280)(101,282)(102,281)(103,277)(104,279)(105,278)(106,306)(107,305)(108,304)(109,303)(110,302)(111,301)(112,315)(113,314)(114,313)(115,312)(116,311)(117,310)(118,309)(119,308)(120,307)(121,291)(122,290)(123,289)(124,288)(125,287)(126,286)(127,300)(128,299)(129,298)(130,297)(131,296)(132,295)(133,294)(134,293)(135,292)(136,319)(137,321)(138,320)(139,316)(140,318)(141,317)(142,328)(143,330)(144,329)(145,325)(146,327)(147,326)(148,322)(149,324)(150,323)(151,351)(152,350)(153,349)(154,348)(155,347)(156,346)(157,360)(158,359)(159,358)(160,357)(161,356)(162,355)(163,354)(164,353)(165,352)(166,336)(167,335)(168,334)(169,333)(170,332)(171,331)(172,345)(173,344)(174,343)(175,342)(176,341)(177,340)(178,339)(179,338)(180,337);;
s2 := (  1, 16)(  2, 18)(  3, 17)(  4, 19)(  5, 21)(  6, 20)(  7, 22)(  8, 24)(  9, 23)( 10, 25)( 11, 27)( 12, 26)( 13, 28)( 14, 30)( 15, 29)( 31, 33)( 34, 36)( 37, 39)( 40, 42)( 43, 45)( 46, 61)( 47, 63)( 48, 62)( 49, 64)( 50, 66)( 51, 65)( 52, 67)( 53, 69)( 54, 68)( 55, 70)( 56, 72)( 57, 71)( 58, 73)( 59, 75)( 60, 74)( 76, 78)( 79, 81)( 82, 84)( 85, 87)( 88, 90)( 91,106)( 92,108)( 93,107)( 94,109)( 95,111)( 96,110)( 97,112)( 98,114)( 99,113)(100,115)(101,117)(102,116)(103,118)(104,120)(105,119)(121,123)(124,126)(127,129)(130,132)(133,135)(136,151)(137,153)(138,152)(139,154)(140,156)(141,155)(142,157)(143,159)(144,158)(145,160)(146,162)(147,161)(148,163)(149,165)(150,164)(166,168)(169,171)(172,174)(175,177)(178,180)(181,286)(182,288)(183,287)(184,289)(185,291)(186,290)(187,292)(188,294)(189,293)(190,295)(191,297)(192,296)(193,298)(194,300)(195,299)(196,271)(197,273)(198,272)(199,274)(200,276)(201,275)(202,277)(203,279)(204,278)(205,280)(206,282)(207,281)(208,283)(209,285)(210,284)(211,303)(212,302)(213,301)(214,306)(215,305)(216,304)(217,309)(218,308)(219,307)(220,312)(221,311)(222,310)(223,315)(224,314)(225,313)(226,331)(227,333)(228,332)(229,334)(230,336)(231,335)(232,337)(233,339)(234,338)(235,340)(236,342)(237,341)(238,343)(239,345)(240,344)(241,316)(242,318)(243,317)(244,319)(245,321)(246,320)(247,322)(248,324)(249,323)(250,325)(251,327)(252,326)(253,328)(254,330)(255,329)(256,348)(257,347)(258,346)(259,351)(260,350)(261,349)(262,354)(263,353)(264,352)(265,357)(266,356)(267,355)(268,360)(269,359)(270,358);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(360)!(  4, 13)(  5, 14)(  6, 15)(  7, 10)(  8, 11)(  9, 12)( 19, 28)( 20, 29)( 21, 30)( 22, 25)( 23, 26)( 24, 27)( 34, 43)( 35, 44)( 36, 45)( 37, 40)( 38, 41)( 39, 42)( 49, 58)( 50, 59)( 51, 60)( 52, 55)( 53, 56)( 54, 57)( 64, 73)( 65, 74)( 66, 75)( 67, 70)( 68, 71)( 69, 72)( 79, 88)( 80, 89)( 81, 90)( 82, 85)( 83, 86)( 84, 87)( 94,103)( 95,104)( 96,105)( 97,100)( 98,101)( 99,102)(109,118)(110,119)(111,120)(112,115)(113,116)(114,117)(124,133)(125,134)(126,135)(127,130)(128,131)(129,132)(139,148)(140,149)(141,150)(142,145)(143,146)(144,147)(154,163)(155,164)(156,165)(157,160)(158,161)(159,162)(169,178)(170,179)(171,180)(172,175)(173,176)(174,177)(181,226)(182,227)(183,228)(184,238)(185,239)(186,240)(187,235)(188,236)(189,237)(190,232)(191,233)(192,234)(193,229)(194,230)(195,231)(196,241)(197,242)(198,243)(199,253)(200,254)(201,255)(202,250)(203,251)(204,252)(205,247)(206,248)(207,249)(208,244)(209,245)(210,246)(211,256)(212,257)(213,258)(214,268)(215,269)(216,270)(217,265)(218,266)(219,267)(220,262)(221,263)(222,264)(223,259)(224,260)(225,261)(271,316)(272,317)(273,318)(274,328)(275,329)(276,330)(277,325)(278,326)(279,327)(280,322)(281,323)(282,324)(283,319)(284,320)(285,321)(286,331)(287,332)(288,333)(289,343)(290,344)(291,345)(292,340)(293,341)(294,342)(295,337)(296,338)(297,339)(298,334)(299,335)(300,336)(301,346)(302,347)(303,348)(304,358)(305,359)(306,360)(307,355)(308,356)(309,357)(310,352)(311,353)(312,354)(313,349)(314,350)(315,351);
s1 := Sym(360)!(  1,184)(  2,186)(  3,185)(  4,181)(  5,183)(  6,182)(  7,193)(  8,195)(  9,194)( 10,190)( 11,192)( 12,191)( 13,187)( 14,189)( 15,188)( 16,216)( 17,215)( 18,214)( 19,213)( 20,212)( 21,211)( 22,225)( 23,224)( 24,223)( 25,222)( 26,221)( 27,220)( 28,219)( 29,218)( 30,217)( 31,201)( 32,200)( 33,199)( 34,198)( 35,197)( 36,196)( 37,210)( 38,209)( 39,208)( 40,207)( 41,206)( 42,205)( 43,204)( 44,203)( 45,202)( 46,229)( 47,231)( 48,230)( 49,226)( 50,228)( 51,227)( 52,238)( 53,240)( 54,239)( 55,235)( 56,237)( 57,236)( 58,232)( 59,234)( 60,233)( 61,261)( 62,260)( 63,259)( 64,258)( 65,257)( 66,256)( 67,270)( 68,269)( 69,268)( 70,267)( 71,266)( 72,265)( 73,264)( 74,263)( 75,262)( 76,246)( 77,245)( 78,244)( 79,243)( 80,242)( 81,241)( 82,255)( 83,254)( 84,253)( 85,252)( 86,251)( 87,250)( 88,249)( 89,248)( 90,247)( 91,274)( 92,276)( 93,275)( 94,271)( 95,273)( 96,272)( 97,283)( 98,285)( 99,284)(100,280)(101,282)(102,281)(103,277)(104,279)(105,278)(106,306)(107,305)(108,304)(109,303)(110,302)(111,301)(112,315)(113,314)(114,313)(115,312)(116,311)(117,310)(118,309)(119,308)(120,307)(121,291)(122,290)(123,289)(124,288)(125,287)(126,286)(127,300)(128,299)(129,298)(130,297)(131,296)(132,295)(133,294)(134,293)(135,292)(136,319)(137,321)(138,320)(139,316)(140,318)(141,317)(142,328)(143,330)(144,329)(145,325)(146,327)(147,326)(148,322)(149,324)(150,323)(151,351)(152,350)(153,349)(154,348)(155,347)(156,346)(157,360)(158,359)(159,358)(160,357)(161,356)(162,355)(163,354)(164,353)(165,352)(166,336)(167,335)(168,334)(169,333)(170,332)(171,331)(172,345)(173,344)(174,343)(175,342)(176,341)(177,340)(178,339)(179,338)(180,337);
s2 := Sym(360)!(  1, 16)(  2, 18)(  3, 17)(  4, 19)(  5, 21)(  6, 20)(  7, 22)(  8, 24)(  9, 23)( 10, 25)( 11, 27)( 12, 26)( 13, 28)( 14, 30)( 15, 29)( 31, 33)( 34, 36)( 37, 39)( 40, 42)( 43, 45)( 46, 61)( 47, 63)( 48, 62)( 49, 64)( 50, 66)( 51, 65)( 52, 67)( 53, 69)( 54, 68)( 55, 70)( 56, 72)( 57, 71)( 58, 73)( 59, 75)( 60, 74)( 76, 78)( 79, 81)( 82, 84)( 85, 87)( 88, 90)( 91,106)( 92,108)( 93,107)( 94,109)( 95,111)( 96,110)( 97,112)( 98,114)( 99,113)(100,115)(101,117)(102,116)(103,118)(104,120)(105,119)(121,123)(124,126)(127,129)(130,132)(133,135)(136,151)(137,153)(138,152)(139,154)(140,156)(141,155)(142,157)(143,159)(144,158)(145,160)(146,162)(147,161)(148,163)(149,165)(150,164)(166,168)(169,171)(172,174)(175,177)(178,180)(181,286)(182,288)(183,287)(184,289)(185,291)(186,290)(187,292)(188,294)(189,293)(190,295)(191,297)(192,296)(193,298)(194,300)(195,299)(196,271)(197,273)(198,272)(199,274)(200,276)(201,275)(202,277)(203,279)(204,278)(205,280)(206,282)(207,281)(208,283)(209,285)(210,284)(211,303)(212,302)(213,301)(214,306)(215,305)(216,304)(217,309)(218,308)(219,307)(220,312)(221,311)(222,310)(223,315)(224,314)(225,313)(226,331)(227,333)(228,332)(229,334)(230,336)(231,335)(232,337)(233,339)(234,338)(235,340)(236,342)(237,341)(238,343)(239,345)(240,344)(241,316)(242,318)(243,317)(244,319)(245,321)(246,320)(247,322)(248,324)(249,323)(250,325)(251,327)(252,326)(253,328)(254,330)(255,329)(256,348)(257,347)(258,346)(259,351)(260,350)(261,349)(262,354)(263,353)(264,352)(265,357)(266,356)(267,355)(268,360)(269,359)(270,358);
poly := sub<Sym(360)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 >;
References : None.
to this polytope

Twisty Puzzle