Polytope of Type {4,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12}*768g
if this polytope has a name.
Group : SmallGroup(768,1088556)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 32, 192, 96
Order of s0s1s2 : 6
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6}*384a
   4-fold quotients : {4,6}*192a
   8-fold quotients : {4,6}*96
   16-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {4,3}*24, {2,6}*24
   64-fold quotients : {2,3}*12
   96-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*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2, s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 8.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2, s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 8.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2> of order 8.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24

Permutation Representation (GAP) : 
s0 := (  1,221)(  2,222)(  3,224)(  4,223)(  5,218)(  6,217)(  7,219)(  8,220)(  9,213)( 10,214)( 11,216)( 12,215)( 13,210)( 14,209)( 15,211)( 16,212)( 17,205)( 18,206)( 19,208)( 20,207)( 21,202)( 22,201)( 23,203)( 24,204)( 25,197)( 26,198)( 27,200)( 28,199)( 29,194)( 30,193)( 31,195)( 32,196)( 33,253)( 34,254)( 35,256)( 36,255)( 37,250)( 38,249)( 39,251)( 40,252)( 41,245)( 42,246)( 43,248)( 44,247)( 45,242)( 46,241)( 47,243)( 48,244)( 49,237)( 50,238)( 51,240)( 52,239)( 53,234)( 54,233)( 55,235)( 56,236)( 57,229)( 58,230)( 59,232)( 60,231)( 61,226)( 62,225)( 63,227)( 64,228)( 65,285)( 66,286)( 67,288)( 68,287)( 69,282)( 70,281)( 71,283)( 72,284)( 73,277)( 74,278)( 75,280)( 76,279)( 77,274)( 78,273)( 79,275)( 80,276)( 81,269)( 82,270)( 83,272)( 84,271)( 85,266)( 86,265)( 87,267)( 88,268)( 89,261)( 90,262)( 91,264)( 92,263)( 93,258)( 94,257)( 95,259)( 96,260)( 97,317)( 98,318)( 99,320)(100,319)(101,314)(102,313)(103,315)(104,316)(105,309)(106,310)(107,312)(108,311)(109,306)(110,305)(111,307)(112,308)(113,301)(114,302)(115,304)(116,303)(117,298)(118,297)(119,299)(120,300)(121,293)(122,294)(123,296)(124,295)(125,290)(126,289)(127,291)(128,292)(129,349)(130,350)(131,352)(132,351)(133,346)(134,345)(135,347)(136,348)(137,341)(138,342)(139,344)(140,343)(141,338)(142,337)(143,339)(144,340)(145,333)(146,334)(147,336)(148,335)(149,330)(150,329)(151,331)(152,332)(153,325)(154,326)(155,328)(156,327)(157,322)(158,321)(159,323)(160,324)(161,381)(162,382)(163,384)(164,383)(165,378)(166,377)(167,379)(168,380)(169,373)(170,374)(171,376)(172,375)(173,370)(174,369)(175,371)(176,372)(177,365)(178,366)(179,368)(180,367)(181,362)(182,361)(183,363)(184,364)(185,357)(186,358)(187,360)(188,359)(189,354)(190,353)(191,355)(192,356);;
s1 := (  5,  7)(  6,  8)( 13, 15)( 14, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 73)( 42, 74)( 43, 75)( 44, 76)( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 89)( 50, 90)( 51, 91)( 52, 92)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)( 58, 82)( 59, 83)( 60, 84)( 61, 87)( 62, 88)( 63, 85)( 64, 86)(101,103)(102,104)(109,111)(110,112)(113,121)(114,122)(115,123)(116,124)(117,127)(118,128)(119,125)(120,126)(129,161)(130,162)(131,163)(132,164)(133,167)(134,168)(135,165)(136,166)(137,169)(138,170)(139,171)(140,172)(141,175)(142,176)(143,173)(144,174)(145,185)(146,186)(147,187)(148,188)(149,191)(150,192)(151,189)(152,190)(153,177)(154,178)(155,179)(156,180)(157,183)(158,184)(159,181)(160,182)(193,194)(195,196)(197,200)(198,199)(201,202)(203,204)(205,208)(206,207)(209,218)(210,217)(211,220)(212,219)(213,224)(214,223)(215,222)(216,221)(225,258)(226,257)(227,260)(228,259)(229,264)(230,263)(231,262)(232,261)(233,266)(234,265)(235,268)(236,267)(237,272)(238,271)(239,270)(240,269)(241,282)(242,281)(243,284)(244,283)(245,288)(246,287)(247,286)(248,285)(249,274)(250,273)(251,276)(252,275)(253,280)(254,279)(255,278)(256,277)(289,290)(291,292)(293,296)(294,295)(297,298)(299,300)(301,304)(302,303)(305,314)(306,313)(307,316)(308,315)(309,320)(310,319)(311,318)(312,317)(321,354)(322,353)(323,356)(324,355)(325,360)(326,359)(327,358)(328,357)(329,362)(330,361)(331,364)(332,363)(333,368)(334,367)(335,366)(336,365)(337,378)(338,377)(339,380)(340,379)(341,384)(342,383)(343,382)(344,381)(345,370)(346,369)(347,372)(348,371)(349,376)(350,375)(351,374)(352,373);;
s2 := (  1,354)(  2,353)(  3,358)(  4,357)(  5,356)(  6,355)(  7,360)(  8,359)(  9,373)( 10,374)( 11,369)( 12,370)( 13,375)( 14,376)( 15,371)( 16,372)( 17,363)( 18,364)( 19,367)( 20,368)( 21,361)( 22,362)( 23,365)( 24,366)( 25,383)( 26,384)( 27,379)( 28,380)( 29,381)( 30,382)( 31,377)( 32,378)( 33,322)( 34,321)( 35,326)( 36,325)( 37,324)( 38,323)( 39,328)( 40,327)( 41,341)( 42,342)( 43,337)( 44,338)( 45,343)( 46,344)( 47,339)( 48,340)( 49,331)( 50,332)( 51,335)( 52,336)( 53,329)( 54,330)( 55,333)( 56,334)( 57,351)( 58,352)( 59,347)( 60,348)( 61,349)( 62,350)( 63,345)( 64,346)( 65,290)( 66,289)( 67,294)( 68,293)( 69,292)( 70,291)( 71,296)( 72,295)( 73,309)( 74,310)( 75,305)( 76,306)( 77,311)( 78,312)( 79,307)( 80,308)( 81,299)( 82,300)( 83,303)( 84,304)( 85,297)( 86,298)( 87,301)( 88,302)( 89,319)( 90,320)( 91,315)( 92,316)( 93,317)( 94,318)( 95,313)( 96,314)( 97,258)( 98,257)( 99,262)(100,261)(101,260)(102,259)(103,264)(104,263)(105,277)(106,278)(107,273)(108,274)(109,279)(110,280)(111,275)(112,276)(113,267)(114,268)(115,271)(116,272)(117,265)(118,266)(119,269)(120,270)(121,287)(122,288)(123,283)(124,284)(125,285)(126,286)(127,281)(128,282)(129,226)(130,225)(131,230)(132,229)(133,228)(134,227)(135,232)(136,231)(137,245)(138,246)(139,241)(140,242)(141,247)(142,248)(143,243)(144,244)(145,235)(146,236)(147,239)(148,240)(149,233)(150,234)(151,237)(152,238)(153,255)(154,256)(155,251)(156,252)(157,253)(158,254)(159,249)(160,250)(161,194)(162,193)(163,198)(164,197)(165,196)(166,195)(167,200)(168,199)(169,213)(170,214)(171,209)(172,210)(173,215)(174,216)(175,211)(176,212)(177,203)(178,204)(179,207)(180,208)(181,201)(182,202)(183,205)(184,206)(185,223)(186,224)(187,219)(188,220)(189,221)(190,222)(191,217)(192,218);;
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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(384)!(  1,221)(  2,222)(  3,224)(  4,223)(  5,218)(  6,217)(  7,219)(  8,220)(  9,213)( 10,214)( 11,216)( 12,215)( 13,210)( 14,209)( 15,211)( 16,212)( 17,205)( 18,206)( 19,208)( 20,207)( 21,202)( 22,201)( 23,203)( 24,204)( 25,197)( 26,198)( 27,200)( 28,199)( 29,194)( 30,193)( 31,195)( 32,196)( 33,253)( 34,254)( 35,256)( 36,255)( 37,250)( 38,249)( 39,251)( 40,252)( 41,245)( 42,246)( 43,248)( 44,247)( 45,242)( 46,241)( 47,243)( 48,244)( 49,237)( 50,238)( 51,240)( 52,239)( 53,234)( 54,233)( 55,235)( 56,236)( 57,229)( 58,230)( 59,232)( 60,231)( 61,226)( 62,225)( 63,227)( 64,228)( 65,285)( 66,286)( 67,288)( 68,287)( 69,282)( 70,281)( 71,283)( 72,284)( 73,277)( 74,278)( 75,280)( 76,279)( 77,274)( 78,273)( 79,275)( 80,276)( 81,269)( 82,270)( 83,272)( 84,271)( 85,266)( 86,265)( 87,267)( 88,268)( 89,261)( 90,262)( 91,264)( 92,263)( 93,258)( 94,257)( 95,259)( 96,260)( 97,317)( 98,318)( 99,320)(100,319)(101,314)(102,313)(103,315)(104,316)(105,309)(106,310)(107,312)(108,311)(109,306)(110,305)(111,307)(112,308)(113,301)(114,302)(115,304)(116,303)(117,298)(118,297)(119,299)(120,300)(121,293)(122,294)(123,296)(124,295)(125,290)(126,289)(127,291)(128,292)(129,349)(130,350)(131,352)(132,351)(133,346)(134,345)(135,347)(136,348)(137,341)(138,342)(139,344)(140,343)(141,338)(142,337)(143,339)(144,340)(145,333)(146,334)(147,336)(148,335)(149,330)(150,329)(151,331)(152,332)(153,325)(154,326)(155,328)(156,327)(157,322)(158,321)(159,323)(160,324)(161,381)(162,382)(163,384)(164,383)(165,378)(166,377)(167,379)(168,380)(169,373)(170,374)(171,376)(172,375)(173,370)(174,369)(175,371)(176,372)(177,365)(178,366)(179,368)(180,367)(181,362)(182,361)(183,363)(184,364)(185,357)(186,358)(187,360)(188,359)(189,354)(190,353)(191,355)(192,356);
s1 := Sym(384)!(  5,  7)(  6,  8)( 13, 15)( 14, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 73)( 42, 74)( 43, 75)( 44, 76)( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 89)( 50, 90)( 51, 91)( 52, 92)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)( 58, 82)( 59, 83)( 60, 84)( 61, 87)( 62, 88)( 63, 85)( 64, 86)(101,103)(102,104)(109,111)(110,112)(113,121)(114,122)(115,123)(116,124)(117,127)(118,128)(119,125)(120,126)(129,161)(130,162)(131,163)(132,164)(133,167)(134,168)(135,165)(136,166)(137,169)(138,170)(139,171)(140,172)(141,175)(142,176)(143,173)(144,174)(145,185)(146,186)(147,187)(148,188)(149,191)(150,192)(151,189)(152,190)(153,177)(154,178)(155,179)(156,180)(157,183)(158,184)(159,181)(160,182)(193,194)(195,196)(197,200)(198,199)(201,202)(203,204)(205,208)(206,207)(209,218)(210,217)(211,220)(212,219)(213,224)(214,223)(215,222)(216,221)(225,258)(226,257)(227,260)(228,259)(229,264)(230,263)(231,262)(232,261)(233,266)(234,265)(235,268)(236,267)(237,272)(238,271)(239,270)(240,269)(241,282)(242,281)(243,284)(244,283)(245,288)(246,287)(247,286)(248,285)(249,274)(250,273)(251,276)(252,275)(253,280)(254,279)(255,278)(256,277)(289,290)(291,292)(293,296)(294,295)(297,298)(299,300)(301,304)(302,303)(305,314)(306,313)(307,316)(308,315)(309,320)(310,319)(311,318)(312,317)(321,354)(322,353)(323,356)(324,355)(325,360)(326,359)(327,358)(328,357)(329,362)(330,361)(331,364)(332,363)(333,368)(334,367)(335,366)(336,365)(337,378)(338,377)(339,380)(340,379)(341,384)(342,383)(343,382)(344,381)(345,370)(346,369)(347,372)(348,371)(349,376)(350,375)(351,374)(352,373);
s2 := Sym(384)!(  1,354)(  2,353)(  3,358)(  4,357)(  5,356)(  6,355)(  7,360)(  8,359)(  9,373)( 10,374)( 11,369)( 12,370)( 13,375)( 14,376)( 15,371)( 16,372)( 17,363)( 18,364)( 19,367)( 20,368)( 21,361)( 22,362)( 23,365)( 24,366)( 25,383)( 26,384)( 27,379)( 28,380)( 29,381)( 30,382)( 31,377)( 32,378)( 33,322)( 34,321)( 35,326)( 36,325)( 37,324)( 38,323)( 39,328)( 40,327)( 41,341)( 42,342)( 43,337)( 44,338)( 45,343)( 46,344)( 47,339)( 48,340)( 49,331)( 50,332)( 51,335)( 52,336)( 53,329)( 54,330)( 55,333)( 56,334)( 57,351)( 58,352)( 59,347)( 60,348)( 61,349)( 62,350)( 63,345)( 64,346)( 65,290)( 66,289)( 67,294)( 68,293)( 69,292)( 70,291)( 71,296)( 72,295)( 73,309)( 74,310)( 75,305)( 76,306)( 77,311)( 78,312)( 79,307)( 80,308)( 81,299)( 82,300)( 83,303)( 84,304)( 85,297)( 86,298)( 87,301)( 88,302)( 89,319)( 90,320)( 91,315)( 92,316)( 93,317)( 94,318)( 95,313)( 96,314)( 97,258)( 98,257)( 99,262)(100,261)(101,260)(102,259)(103,264)(104,263)(105,277)(106,278)(107,273)(108,274)(109,279)(110,280)(111,275)(112,276)(113,267)(114,268)(115,271)(116,272)(117,265)(118,266)(119,269)(120,270)(121,287)(122,288)(123,283)(124,284)(125,285)(126,286)(127,281)(128,282)(129,226)(130,225)(131,230)(132,229)(133,228)(134,227)(135,232)(136,231)(137,245)(138,246)(139,241)(140,242)(141,247)(142,248)(143,243)(144,244)(145,235)(146,236)(147,239)(148,240)(149,233)(150,234)(151,237)(152,238)(153,255)(154,256)(155,251)(156,252)(157,253)(158,254)(159,249)(160,250)(161,194)(162,193)(163,198)(164,197)(165,196)(166,195)(167,200)(168,199)(169,213)(170,214)(171,209)(172,210)(173,215)(174,216)(175,211)(176,212)(177,203)(178,204)(179,207)(180,208)(181,201)(182,202)(183,205)(184,206)(185,223)(186,224)(187,219)(188,220)(189,221)(190,222)(191,217)(192,218);
poly := sub<Sym(384)|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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle