Polytope of Type {12,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*768p
if this polytope has a name.
Group : SmallGroup(768,1086857)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 48, 192, 32
Order of s0s1s2 : 24
Order of s0s1s2s1 : 8
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 : {6,8}*384f, {12,4}*384e
   4-fold quotients : {6,4}*192b, {6,8}*192b, {6,8}*192c
   8-fold quotients : {3,8}*96, {6,4}*96
   16-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,4}*24, {6,2}*24
   48-fold quotients : {2,4}*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):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      16 facets:
         8 of {4}*8
         8 of {12}*24
      16 vertex figures:
         16 of {8}*16

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

Twisty Puzzle