Polytope of Type {4,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*768e
if this polytope has a name.
Group : SmallGroup(768,1085644)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 16, 192, 96
Order of s0s1s2 : 24
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
   4-fold quotients : {4,6}*192a, {4,24}*192c
   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*s1*s0*s1> of order 2.
      56 facets:
         16 of {2}*4
         40 of {4}*8
      8 vertex figures:
         8 of {24}*48
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      8 vertex figures:
         8 of {24}*48
   P/N, where N=<s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      8 vertex figures:
         8 of {24}*48
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 4.
      32 facets:
         16 of {2}*4
         16 of {4}*8
      4 vertex figures:
         4 of {24}*48
   P/N, where N=<s0*s1*s0*s1, s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 4.
      36 facets:
         24 of {2}*4
         12 of {4}*8
      4 vertex figures:
         4 of {24}*48
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      4 vertex figures:
         4 of {24}*48

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