Polytope of Type {24,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*768k
if this polytope has a name.
Group : SmallGroup(768,1086615)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 48, 192, 16
Order of s0s1s2 : 24
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
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 : {12,8}*384f, {24,4}*384c
   4-fold quotients : {24,4}*192c, {24,4}*192d, {12,4}*192b, {6,8}*192c
   8-fold quotients : {24,2}*96, {12,4}*96b, {12,4}*96c, {6,4}*96
   16-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   24-fold quotients : {8,2}*32
   32-fold quotients : {3,4}*24, {6,2}*24
   48-fold quotients : {4,2}*16
   64-fold quotients : {3,2}*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):
   None.

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

Twisty Puzzle