Polytope of Type {12,30}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,30}*1440b
if this polytope has a name.
Group : SmallGroup(1440,5900)
Rank : 3
Schlafli Type : {12,30}
Number of vertices, edges, etc : 24, 360, 60
Order of s0s1s2 : 30
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {12,15}*720
   3-fold quotients : {4,30}*480
   4-fold quotients : {6,30}*360c
   5-fold quotients : {12,6}*288b
   6-fold quotients : {4,15}*240, {4,30}*240b, {4,30}*240c
   8-fold quotients : {6,15}*180
   10-fold quotients : {12,3}*144
   12-fold quotients : {4,15}*120, {2,30}*120
   15-fold quotients : {4,6}*96
   20-fold quotients : {6,6}*72b
   24-fold quotients : {2,15}*60
   30-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   36-fold quotients : {2,10}*40
   40-fold quotients : {6,3}*36
   60-fold quotients : {4,3}*24, {2,6}*24
   72-fold quotients : {2,5}*20
   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):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 2.
      40 facets:
         20 of {6}*12
         20 of {12}*24
      12 vertex figures:
         12 of {30}*60
   P/N, where N=<s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 2.
      30 facets:
         30 of {12}*24
      12 vertex figures:
         12 of {30}*60
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      30 facets:
         30 of {12}*24
      12 vertex figures:
         12 of {30}*60

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