Polytope of Type {8,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*768e
if this polytope has a name.
Group : SmallGroup(768,1086012)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 32, 192, 48
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {4,12}*384b, {8,6}*384b
   4-fold quotients : {4,6}*192a
   8-fold quotients : {4,12}*96b
   16-fold quotients : {4,6}*48c
   32-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 2.
      24 facets:
         24 of {8}*16
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1> of order 2.
      24 facets:
         24 of {8}*16
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
      12 facets:
         12 of {8}*16
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      12 facets:
         12 of {8}*16
      8 vertex figures:
         8 of {12}*24

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

Twisty Puzzle