Polytope of Type {8,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*768c
if this polytope has a name.
Group : SmallGroup(768,90301)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 32, 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 : {4,12}*384a
   3-fold quotients : {8,4}*256c
   4-fold quotients : {4,12}*192a
   6-fold quotients : {4,4}*128
   8-fold quotients : {4,12}*96a
   12-fold quotients : {4,4}*64
   16-fold quotients : {2,12}*48, {4,6}*48a
   24-fold quotients : {4,4}*32
   32-fold quotients : {2,6}*24
   48-fold quotients : {2,4}*16, {4,2}*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):
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 2.
      24 facets:
         24 of {8}*16
      16 vertex figures:
         16 of {12}*24

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