Polytope of Type {12,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*768b
if this polytope has a name.
Group : SmallGroup(768,1086909)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 16, 192, 32
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {12,12}*384c, {6,24}*384b
   4-fold quotients : {6,12}*192a, {12,6}*192b
   8-fold quotients : {12,3}*96, {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   32-fold quotients : {3,3}*24
   48-fold quotients : {2,4}*16
   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 := (  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)( 51, 52)( 53, 55)( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)( 63, 69)( 64, 70)( 75, 76)( 77, 79)( 78, 80)( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 97,122)( 98,121)( 99,123)(100,124)(101,128)(102,127)(103,126)(104,125)(105,138)(106,137)(107,139)(108,140)(109,144)(110,143)(111,142)(112,141)(113,130)(114,129)(115,131)(116,132)(117,136)(118,135)(119,134)(120,133)(145,170)(146,169)(147,171)(148,172)(149,176)(150,175)(151,174)(152,173)(153,186)(154,185)(155,187)(156,188)(157,192)(158,191)(159,190)(160,189)(161,178)(162,177)(163,179)(164,180)(165,184)(166,183)(167,182)(168,181)(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)(241,242)(245,248)(246,247)(249,258)(250,257)(251,259)(252,260)(253,264)(254,263)(255,262)(256,261)(265,266)(269,272)(270,271)(273,282)(274,281)(275,283)(276,284)(277,288)(278,287)(279,286)(280,285)(289,313)(290,314)(291,316)(292,315)(293,319)(294,320)(295,317)(296,318)(297,329)(298,330)(299,332)(300,331)(301,335)(302,336)(303,333)(304,334)(305,321)(306,322)(307,324)(308,323)(309,327)(310,328)(311,325)(312,326)(337,361)(338,362)(339,364)(340,363)(341,367)(342,368)(343,365)(344,366)(345,377)(346,378)(347,380)(348,379)(349,383)(350,384)(351,381)(352,382)(353,369)(354,370)(355,372)(356,371)(357,375)(358,376)(359,373)(360,374);;
s1 := (  1,138)(  2,137)(  3,141)(  4,142)(  5,139)(  6,140)(  7,143)(  8,144)(  9,130)( 10,129)( 11,133)( 12,134)( 13,131)( 14,132)( 15,135)( 16,136)( 17,122)( 18,121)( 19,125)( 20,126)( 21,123)( 22,124)( 23,127)( 24,128)( 25,114)( 26,113)( 27,117)( 28,118)( 29,115)( 30,116)( 31,119)( 32,120)( 33,106)( 34,105)( 35,109)( 36,110)( 37,107)( 38,108)( 39,111)( 40,112)( 41, 98)( 42, 97)( 43,101)( 44,102)( 45, 99)( 46,100)( 47,103)( 48,104)( 49,162)( 50,161)( 51,165)( 52,166)( 53,163)( 54,164)( 55,167)( 56,168)( 57,154)( 58,153)( 59,157)( 60,158)( 61,155)( 62,156)( 63,159)( 64,160)( 65,146)( 66,145)( 67,149)( 68,150)( 69,147)( 70,148)( 71,151)( 72,152)( 73,186)( 74,185)( 75,189)( 76,190)( 77,187)( 78,188)( 79,191)( 80,192)( 81,178)( 82,177)( 83,181)( 84,182)( 85,179)( 86,180)( 87,183)( 88,184)( 89,170)( 90,169)( 91,173)( 92,174)( 93,171)( 94,172)( 95,175)( 96,176)(193,329)(194,330)(195,334)(196,333)(197,332)(198,331)(199,336)(200,335)(201,321)(202,322)(203,326)(204,325)(205,324)(206,323)(207,328)(208,327)(209,313)(210,314)(211,318)(212,317)(213,316)(214,315)(215,320)(216,319)(217,305)(218,306)(219,310)(220,309)(221,308)(222,307)(223,312)(224,311)(225,297)(226,298)(227,302)(228,301)(229,300)(230,299)(231,304)(232,303)(233,289)(234,290)(235,294)(236,293)(237,292)(238,291)(239,296)(240,295)(241,353)(242,354)(243,358)(244,357)(245,356)(246,355)(247,360)(248,359)(249,345)(250,346)(251,350)(252,349)(253,348)(254,347)(255,352)(256,351)(257,337)(258,338)(259,342)(260,341)(261,340)(262,339)(263,344)(264,343)(265,377)(266,378)(267,382)(268,381)(269,380)(270,379)(271,384)(272,383)(273,369)(274,370)(275,374)(276,373)(277,372)(278,371)(279,376)(280,375)(281,361)(282,362)(283,366)(284,365)(285,364)(286,363)(287,368)(288,367);;
s2 := (  1,195)(  2,196)(  3,193)(  4,194)(  5,198)(  6,197)(  7,199)(  8,200)(  9,211)( 10,212)( 11,209)( 12,210)( 13,214)( 14,213)( 15,215)( 16,216)( 17,203)( 18,204)( 19,201)( 20,202)( 21,206)( 22,205)( 23,207)( 24,208)( 25,219)( 26,220)( 27,217)( 28,218)( 29,222)( 30,221)( 31,223)( 32,224)( 33,235)( 34,236)( 35,233)( 36,234)( 37,238)( 38,237)( 39,239)( 40,240)( 41,227)( 42,228)( 43,225)( 44,226)( 45,230)( 46,229)( 47,231)( 48,232)( 49,267)( 50,268)( 51,265)( 52,266)( 53,270)( 54,269)( 55,271)( 56,272)( 57,283)( 58,284)( 59,281)( 60,282)( 61,286)( 62,285)( 63,287)( 64,288)( 65,275)( 66,276)( 67,273)( 68,274)( 69,278)( 70,277)( 71,279)( 72,280)( 73,243)( 74,244)( 75,241)( 76,242)( 77,246)( 78,245)( 79,247)( 80,248)( 81,259)( 82,260)( 83,257)( 84,258)( 85,262)( 86,261)( 87,263)( 88,264)( 89,251)( 90,252)( 91,249)( 92,250)( 93,254)( 94,253)( 95,255)( 96,256)( 97,364)( 98,363)( 99,362)(100,361)(101,365)(102,366)(103,368)(104,367)(105,380)(106,379)(107,378)(108,377)(109,381)(110,382)(111,384)(112,383)(113,372)(114,371)(115,370)(116,369)(117,373)(118,374)(119,376)(120,375)(121,340)(122,339)(123,338)(124,337)(125,341)(126,342)(127,344)(128,343)(129,356)(130,355)(131,354)(132,353)(133,357)(134,358)(135,360)(136,359)(137,348)(138,347)(139,346)(140,345)(141,349)(142,350)(143,352)(144,351)(145,316)(146,315)(147,314)(148,313)(149,317)(150,318)(151,320)(152,319)(153,332)(154,331)(155,330)(156,329)(157,333)(158,334)(159,336)(160,335)(161,324)(162,323)(163,322)(164,321)(165,325)(166,326)(167,328)(168,327)(169,292)(170,291)(171,290)(172,289)(173,293)(174,294)(175,296)(176,295)(177,308)(178,307)(179,306)(180,305)(181,309)(182,310)(183,312)(184,311)(185,300)(186,299)(187,298)(188,297)(189,301)(190,302)(191,304)(192,303);;
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*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := 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)( 51, 52)( 53, 55)( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)( 63, 69)( 64, 70)( 75, 76)( 77, 79)( 78, 80)( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 97,122)( 98,121)( 99,123)(100,124)(101,128)(102,127)(103,126)(104,125)(105,138)(106,137)(107,139)(108,140)(109,144)(110,143)(111,142)(112,141)(113,130)(114,129)(115,131)(116,132)(117,136)(118,135)(119,134)(120,133)(145,170)(146,169)(147,171)(148,172)(149,176)(150,175)(151,174)(152,173)(153,186)(154,185)(155,187)(156,188)(157,192)(158,191)(159,190)(160,189)(161,178)(162,177)(163,179)(164,180)(165,184)(166,183)(167,182)(168,181)(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)(241,242)(245,248)(246,247)(249,258)(250,257)(251,259)(252,260)(253,264)(254,263)(255,262)(256,261)(265,266)(269,272)(270,271)(273,282)(274,281)(275,283)(276,284)(277,288)(278,287)(279,286)(280,285)(289,313)(290,314)(291,316)(292,315)(293,319)(294,320)(295,317)(296,318)(297,329)(298,330)(299,332)(300,331)(301,335)(302,336)(303,333)(304,334)(305,321)(306,322)(307,324)(308,323)(309,327)(310,328)(311,325)(312,326)(337,361)(338,362)(339,364)(340,363)(341,367)(342,368)(343,365)(344,366)(345,377)(346,378)(347,380)(348,379)(349,383)(350,384)(351,381)(352,382)(353,369)(354,370)(355,372)(356,371)(357,375)(358,376)(359,373)(360,374);
s1 := Sym(384)!(  1,138)(  2,137)(  3,141)(  4,142)(  5,139)(  6,140)(  7,143)(  8,144)(  9,130)( 10,129)( 11,133)( 12,134)( 13,131)( 14,132)( 15,135)( 16,136)( 17,122)( 18,121)( 19,125)( 20,126)( 21,123)( 22,124)( 23,127)( 24,128)( 25,114)( 26,113)( 27,117)( 28,118)( 29,115)( 30,116)( 31,119)( 32,120)( 33,106)( 34,105)( 35,109)( 36,110)( 37,107)( 38,108)( 39,111)( 40,112)( 41, 98)( 42, 97)( 43,101)( 44,102)( 45, 99)( 46,100)( 47,103)( 48,104)( 49,162)( 50,161)( 51,165)( 52,166)( 53,163)( 54,164)( 55,167)( 56,168)( 57,154)( 58,153)( 59,157)( 60,158)( 61,155)( 62,156)( 63,159)( 64,160)( 65,146)( 66,145)( 67,149)( 68,150)( 69,147)( 70,148)( 71,151)( 72,152)( 73,186)( 74,185)( 75,189)( 76,190)( 77,187)( 78,188)( 79,191)( 80,192)( 81,178)( 82,177)( 83,181)( 84,182)( 85,179)( 86,180)( 87,183)( 88,184)( 89,170)( 90,169)( 91,173)( 92,174)( 93,171)( 94,172)( 95,175)( 96,176)(193,329)(194,330)(195,334)(196,333)(197,332)(198,331)(199,336)(200,335)(201,321)(202,322)(203,326)(204,325)(205,324)(206,323)(207,328)(208,327)(209,313)(210,314)(211,318)(212,317)(213,316)(214,315)(215,320)(216,319)(217,305)(218,306)(219,310)(220,309)(221,308)(222,307)(223,312)(224,311)(225,297)(226,298)(227,302)(228,301)(229,300)(230,299)(231,304)(232,303)(233,289)(234,290)(235,294)(236,293)(237,292)(238,291)(239,296)(240,295)(241,353)(242,354)(243,358)(244,357)(245,356)(246,355)(247,360)(248,359)(249,345)(250,346)(251,350)(252,349)(253,348)(254,347)(255,352)(256,351)(257,337)(258,338)(259,342)(260,341)(261,340)(262,339)(263,344)(264,343)(265,377)(266,378)(267,382)(268,381)(269,380)(270,379)(271,384)(272,383)(273,369)(274,370)(275,374)(276,373)(277,372)(278,371)(279,376)(280,375)(281,361)(282,362)(283,366)(284,365)(285,364)(286,363)(287,368)(288,367);
s2 := Sym(384)!(  1,195)(  2,196)(  3,193)(  4,194)(  5,198)(  6,197)(  7,199)(  8,200)(  9,211)( 10,212)( 11,209)( 12,210)( 13,214)( 14,213)( 15,215)( 16,216)( 17,203)( 18,204)( 19,201)( 20,202)( 21,206)( 22,205)( 23,207)( 24,208)( 25,219)( 26,220)( 27,217)( 28,218)( 29,222)( 30,221)( 31,223)( 32,224)( 33,235)( 34,236)( 35,233)( 36,234)( 37,238)( 38,237)( 39,239)( 40,240)( 41,227)( 42,228)( 43,225)( 44,226)( 45,230)( 46,229)( 47,231)( 48,232)( 49,267)( 50,268)( 51,265)( 52,266)( 53,270)( 54,269)( 55,271)( 56,272)( 57,283)( 58,284)( 59,281)( 60,282)( 61,286)( 62,285)( 63,287)( 64,288)( 65,275)( 66,276)( 67,273)( 68,274)( 69,278)( 70,277)( 71,279)( 72,280)( 73,243)( 74,244)( 75,241)( 76,242)( 77,246)( 78,245)( 79,247)( 80,248)( 81,259)( 82,260)( 83,257)( 84,258)( 85,262)( 86,261)( 87,263)( 88,264)( 89,251)( 90,252)( 91,249)( 92,250)( 93,254)( 94,253)( 95,255)( 96,256)( 97,364)( 98,363)( 99,362)(100,361)(101,365)(102,366)(103,368)(104,367)(105,380)(106,379)(107,378)(108,377)(109,381)(110,382)(111,384)(112,383)(113,372)(114,371)(115,370)(116,369)(117,373)(118,374)(119,376)(120,375)(121,340)(122,339)(123,338)(124,337)(125,341)(126,342)(127,344)(128,343)(129,356)(130,355)(131,354)(132,353)(133,357)(134,358)(135,360)(136,359)(137,348)(138,347)(139,346)(140,345)(141,349)(142,350)(143,352)(144,351)(145,316)(146,315)(147,314)(148,313)(149,317)(150,318)(151,320)(152,319)(153,332)(154,331)(155,330)(156,329)(157,333)(158,334)(159,336)(160,335)(161,324)(162,323)(163,322)(164,321)(165,325)(166,326)(167,328)(168,327)(169,292)(170,291)(171,290)(172,289)(173,293)(174,294)(175,296)(176,295)(177,308)(178,307)(179,306)(180,305)(181,309)(182,310)(183,312)(184,311)(185,300)(186,299)(187,298)(188,297)(189,301)(190,302)(191,304)(192,303);
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*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1 >;
References : None.
to this polytope

Twisty Puzzle