Polytope of Type {8,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,24}*768i
if this polytope has a name.
Group : SmallGroup(768,1086577)
Rank : 3
Schlafli Type : {8,24}
Number of vertices, edges, etc : 16, 192, 48
Order of s0s1s2 : 24
Order of s0s1s2s1 : 8
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 : {8,12}*384e, {4,24}*384c
   4-fold quotients : {4,24}*192c, {4,24}*192d, {4,12}*192b, {8,6}*192b
   8-fold quotients : {2,24}*96, {4,12}*96b, {4,12}*96c, {8,3}*96, {4,6}*96
   16-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
   24-fold quotients : {2,8}*32
   32-fold quotients : {4,3}*24, {2,6}*24
   48-fold quotients : {2,4}*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):
   None.

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