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}*768j
if this polytope has a name.
Group : SmallGroup(768,1086593)
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}*384d
   4-fold quotients : {4,12}*192b, {8,6}*192b
   8-fold quotients : {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
   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)( 97,319)( 98,320)( 99,317)(100,318)(101,316)(102,315)(103,314)(104,313)(105,327)(106,328)(107,325)(108,326)(109,324)(110,323)(111,322)(112,321)(113,335)(114,336)(115,333)(116,334)(117,332)(118,331)(119,330)(120,329)(121,295)(122,296)(123,293)(124,294)(125,292)(126,291)(127,290)(128,289)(129,303)(130,304)(131,301)(132,302)(133,300)(134,299)(135,298)(136,297)(137,311)(138,312)(139,309)(140,310)(141,308)(142,307)(143,306)(144,305)(145,367)(146,368)(147,365)(148,366)(149,364)(150,363)(151,362)(152,361)(153,375)(154,376)(155,373)(156,374)(157,372)(158,371)(159,370)(160,369)(161,383)(162,384)(163,381)(164,382)(165,380)(166,379)(167,378)(168,377)(169,343)(170,344)(171,341)(172,342)(173,340)(174,339)(175,338)(176,337)(177,351)(178,352)(179,349)(180,350)(181,348)(182,347)(183,346)(184,345)(185,359)(186,360)(187,357)(188,358)(189,356)(190,355)(191,354)(192,353);;
s1 := (  1,362)(  2,361)(  3,363)(  4,364)(  5,368)(  6,367)(  7,366)(  8,365)(  9,378)( 10,377)( 11,379)( 12,380)( 13,384)( 14,383)( 15,382)( 16,381)( 17,370)( 18,369)( 19,371)( 20,372)( 21,376)( 22,375)( 23,374)( 24,373)( 25,338)( 26,337)( 27,339)( 28,340)( 29,344)( 30,343)( 31,342)( 32,341)( 33,354)( 34,353)( 35,355)( 36,356)( 37,360)( 38,359)( 39,358)( 40,357)( 41,346)( 42,345)( 43,347)( 44,348)( 45,352)( 46,351)( 47,350)( 48,349)( 49,314)( 50,313)( 51,315)( 52,316)( 53,320)( 54,319)( 55,318)( 56,317)( 57,330)( 58,329)( 59,331)( 60,332)( 61,336)( 62,335)( 63,334)( 64,333)( 65,322)( 66,321)( 67,323)( 68,324)( 69,328)( 70,327)( 71,326)( 72,325)( 73,290)( 74,289)( 75,291)( 76,292)( 77,296)( 78,295)( 79,294)( 80,293)( 81,306)( 82,305)( 83,307)( 84,308)( 85,312)( 86,311)( 87,310)( 88,309)( 89,298)( 90,297)( 91,299)( 92,300)( 93,304)( 94,303)( 95,302)( 96,301)( 97,266)( 98,265)( 99,267)(100,268)(101,272)(102,271)(103,270)(104,269)(105,282)(106,281)(107,283)(108,284)(109,288)(110,287)(111,286)(112,285)(113,274)(114,273)(115,275)(116,276)(117,280)(118,279)(119,278)(120,277)(121,242)(122,241)(123,243)(124,244)(125,248)(126,247)(127,246)(128,245)(129,258)(130,257)(131,259)(132,260)(133,264)(134,263)(135,262)(136,261)(137,250)(138,249)(139,251)(140,252)(141,256)(142,255)(143,254)(144,253)(145,218)(146,217)(147,219)(148,220)(149,224)(150,223)(151,222)(152,221)(153,234)(154,233)(155,235)(156,236)(157,240)(158,239)(159,238)(160,237)(161,226)(162,225)(163,227)(164,228)(165,232)(166,231)(167,230)(168,229)(169,194)(170,193)(171,195)(172,196)(173,200)(174,199)(175,198)(176,197)(177,210)(178,209)(179,211)(180,212)(181,216)(182,215)(183,214)(184,213)(185,202)(186,201)(187,203)(188,204)(189,208)(190,207)(191,206)(192,205);;
s2 := (  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)(193,210)(194,209)(195,213)(196,214)(197,211)(198,212)(199,215)(200,216)(201,202)(203,205)(204,206)(217,234)(218,233)(219,237)(220,238)(221,235)(222,236)(223,239)(224,240)(225,226)(227,229)(228,230)(241,282)(242,281)(243,285)(244,286)(245,283)(246,284)(247,287)(248,288)(249,274)(250,273)(251,277)(252,278)(253,275)(254,276)(255,279)(256,280)(257,266)(258,265)(259,269)(260,270)(261,267)(262,268)(263,271)(264,272)(289,354)(290,353)(291,357)(292,358)(293,355)(294,356)(295,359)(296,360)(297,346)(298,345)(299,349)(300,350)(301,347)(302,348)(303,351)(304,352)(305,338)(306,337)(307,341)(308,342)(309,339)(310,340)(311,343)(312,344)(313,378)(314,377)(315,381)(316,382)(317,379)(318,380)(319,383)(320,384)(321,370)(322,369)(323,373)(324,374)(325,371)(326,372)(327,375)(328,376)(329,362)(330,361)(331,365)(332,366)(333,363)(334,364)(335,367)(336,368);;
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, 
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*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*s0*s2*s1*s2*s1 ];;
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)( 97,319)( 98,320)( 99,317)(100,318)(101,316)(102,315)(103,314)(104,313)(105,327)(106,328)(107,325)(108,326)(109,324)(110,323)(111,322)(112,321)(113,335)(114,336)(115,333)(116,334)(117,332)(118,331)(119,330)(120,329)(121,295)(122,296)(123,293)(124,294)(125,292)(126,291)(127,290)(128,289)(129,303)(130,304)(131,301)(132,302)(133,300)(134,299)(135,298)(136,297)(137,311)(138,312)(139,309)(140,310)(141,308)(142,307)(143,306)(144,305)(145,367)(146,368)(147,365)(148,366)(149,364)(150,363)(151,362)(152,361)(153,375)(154,376)(155,373)(156,374)(157,372)(158,371)(159,370)(160,369)(161,383)(162,384)(163,381)(164,382)(165,380)(166,379)(167,378)(168,377)(169,343)(170,344)(171,341)(172,342)(173,340)(174,339)(175,338)(176,337)(177,351)(178,352)(179,349)(180,350)(181,348)(182,347)(183,346)(184,345)(185,359)(186,360)(187,357)(188,358)(189,356)(190,355)(191,354)(192,353);
s1 := Sym(384)!(  1,362)(  2,361)(  3,363)(  4,364)(  5,368)(  6,367)(  7,366)(  8,365)(  9,378)( 10,377)( 11,379)( 12,380)( 13,384)( 14,383)( 15,382)( 16,381)( 17,370)( 18,369)( 19,371)( 20,372)( 21,376)( 22,375)( 23,374)( 24,373)( 25,338)( 26,337)( 27,339)( 28,340)( 29,344)( 30,343)( 31,342)( 32,341)( 33,354)( 34,353)( 35,355)( 36,356)( 37,360)( 38,359)( 39,358)( 40,357)( 41,346)( 42,345)( 43,347)( 44,348)( 45,352)( 46,351)( 47,350)( 48,349)( 49,314)( 50,313)( 51,315)( 52,316)( 53,320)( 54,319)( 55,318)( 56,317)( 57,330)( 58,329)( 59,331)( 60,332)( 61,336)( 62,335)( 63,334)( 64,333)( 65,322)( 66,321)( 67,323)( 68,324)( 69,328)( 70,327)( 71,326)( 72,325)( 73,290)( 74,289)( 75,291)( 76,292)( 77,296)( 78,295)( 79,294)( 80,293)( 81,306)( 82,305)( 83,307)( 84,308)( 85,312)( 86,311)( 87,310)( 88,309)( 89,298)( 90,297)( 91,299)( 92,300)( 93,304)( 94,303)( 95,302)( 96,301)( 97,266)( 98,265)( 99,267)(100,268)(101,272)(102,271)(103,270)(104,269)(105,282)(106,281)(107,283)(108,284)(109,288)(110,287)(111,286)(112,285)(113,274)(114,273)(115,275)(116,276)(117,280)(118,279)(119,278)(120,277)(121,242)(122,241)(123,243)(124,244)(125,248)(126,247)(127,246)(128,245)(129,258)(130,257)(131,259)(132,260)(133,264)(134,263)(135,262)(136,261)(137,250)(138,249)(139,251)(140,252)(141,256)(142,255)(143,254)(144,253)(145,218)(146,217)(147,219)(148,220)(149,224)(150,223)(151,222)(152,221)(153,234)(154,233)(155,235)(156,236)(157,240)(158,239)(159,238)(160,237)(161,226)(162,225)(163,227)(164,228)(165,232)(166,231)(167,230)(168,229)(169,194)(170,193)(171,195)(172,196)(173,200)(174,199)(175,198)(176,197)(177,210)(178,209)(179,211)(180,212)(181,216)(182,215)(183,214)(184,213)(185,202)(186,201)(187,203)(188,204)(189,208)(190,207)(191,206)(192,205);
s2 := 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)(193,210)(194,209)(195,213)(196,214)(197,211)(198,212)(199,215)(200,216)(201,202)(203,205)(204,206)(217,234)(218,233)(219,237)(220,238)(221,235)(222,236)(223,239)(224,240)(225,226)(227,229)(228,230)(241,282)(242,281)(243,285)(244,286)(245,283)(246,284)(247,287)(248,288)(249,274)(250,273)(251,277)(252,278)(253,275)(254,276)(255,279)(256,280)(257,266)(258,265)(259,269)(260,270)(261,267)(262,268)(263,271)(264,272)(289,354)(290,353)(291,357)(292,358)(293,355)(294,356)(295,359)(296,360)(297,346)(298,345)(299,349)(300,350)(301,347)(302,348)(303,351)(304,352)(305,338)(306,337)(307,341)(308,342)(309,339)(310,340)(311,343)(312,344)(313,378)(314,377)(315,381)(316,382)(317,379)(318,380)(319,383)(320,384)(321,370)(322,369)(323,373)(324,374)(325,371)(326,372)(327,375)(328,376)(329,362)(330,361)(331,365)(332,366)(333,363)(334,364)(335,367)(336,368);
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, 
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*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*s0*s2*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle