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}*768a
if this polytope has a name.
Group : SmallGroup(768,81599)
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
   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 : {4,24}*384a, {4,12}*384a, {4,24}*384b
   3-fold quotients : {4,8}*256a
   4-fold quotients : {4,24}*192a, {4,12}*192a, {4,24}*192b
   6-fold quotients : {4,8}*128a, {4,4}*128, {4,8}*128b
   8-fold quotients : {4,12}*96a, {2,24}*96
   12-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
   16-fold quotients : {2,12}*48, {4,6}*48a
   24-fold quotients : {4,4}*32, {2,8}*32
   32-fold quotients : {2,6}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   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*s0*s1> of order 2.
      60 facets:
         24 of {2}*4
         36 of {4}*8
      8 vertex figures:
         8 of {24}*48
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      48 facets:
         48 of {4}*8
      8 vertex figures:
         8 of {24}*48
   P/N, where N=<s1*s0*s1*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=<s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*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=<s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*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*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.
      48 facets:
         48 of {4}*8
      8 vertex figures:
         8 of {24}*48
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {4}*8
      4 vertex figures:
         4 of {24}*48
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      4 vertex figures:
         4 of {24}*48
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {4}*8
      4 vertex figures:
         4 of {24}*48
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1> of order 4.
      36 facets:
         24 of {2}*4
         12 of {4}*8
      4 vertex figures:
         4 of {24}*48
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*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 4.
      24 facets:
         24 of {4}*8
      4 vertex figures:
         4 of {24}*48
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {4}*8
      4 vertex figures:
         4 of {24}*48
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*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> of order 4.
      24 facets:
         24 of {4}*8
      4 vertex figures:
         4 of {24}*48
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*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.
      30 facets:
         12 of {2}*4
         18 of {4}*8
      4 vertex figures:
         4 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.
      30 facets:
         12 of {2}*4
         18 of {4}*8
      4 vertex figures:
         4 of {24}*48

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