Polytope of Type {12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*768a
if this polytope has a name.
Group : SmallGroup(768,1087715)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 32, 192, 32
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
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}*384a, {12,12}*384b, {6,12}*384, {12,6}*384, {12,12}*384c, {12,12}*384d
   4-fold quotients : {6,12}*192a, {12,6}*192a, {6,12}*192b, {12,6}*192b, {6,6}*192b
   8-fold quotients : {3,12}*96, {12,3}*96, {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   24-fold quotients : {4,4}*32
   32-fold quotients : {3,3}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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)
( 49,185)( 50,186)( 51,190)( 52,189)( 53,188)( 54,187)( 55,192)( 56,191)
( 57,177)( 58,178)( 59,182)( 60,181)( 61,180)( 62,179)( 63,184)( 64,183)
( 65,169)( 66,170)( 67,174)( 68,173)( 69,172)( 70,171)( 71,176)( 72,175)
( 73,161)( 74,162)( 75,166)( 76,165)( 77,164)( 78,163)( 79,168)( 80,167)
( 81,153)( 82,154)( 83,158)( 84,157)( 85,156)( 86,155)( 87,160)( 88,159)
( 89,145)( 90,146)( 91,150)( 92,149)( 93,148)( 94,147)( 95,152)( 96,151)
(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)
(241,378)(242,377)(243,381)(244,382)(245,379)(246,380)(247,383)(248,384)
(249,370)(250,369)(251,373)(252,374)(253,371)(254,372)(255,375)(256,376)
(257,362)(258,361)(259,365)(260,366)(261,363)(262,364)(263,367)(264,368)
(265,354)(266,353)(267,357)(268,358)(269,355)(270,356)(271,359)(272,360)
(273,346)(274,345)(275,349)(276,350)(277,347)(278,348)(279,351)(280,352)
(281,338)(282,337)(283,341)(284,342)(285,339)(286,340)(287,343)(288,344);;
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)
( 49,243)( 50,244)( 51,241)( 52,242)( 53,246)( 54,245)( 55,247)( 56,248)
( 57,259)( 58,260)( 59,257)( 60,258)( 61,262)( 62,261)( 63,263)( 64,264)
( 65,251)( 66,252)( 67,249)( 68,250)( 69,254)( 70,253)( 71,255)( 72,256)
( 73,267)( 74,268)( 75,265)( 76,266)( 77,270)( 78,269)( 79,271)( 80,272)
( 81,283)( 82,284)( 83,281)( 84,282)( 85,286)( 86,285)( 87,287)( 88,288)
( 89,275)( 90,276)( 91,273)( 92,274)( 93,278)( 94,277)( 95,279)( 96,280)
( 97,363)( 98,364)( 99,361)(100,362)(101,366)(102,365)(103,367)(104,368)
(105,379)(106,380)(107,377)(108,378)(109,382)(110,381)(111,383)(112,384)
(113,371)(114,372)(115,369)(116,370)(117,374)(118,373)(119,375)(120,376)
(121,339)(122,340)(123,337)(124,338)(125,342)(126,341)(127,343)(128,344)
(129,355)(130,356)(131,353)(132,354)(133,358)(134,357)(135,359)(136,360)
(137,347)(138,348)(139,345)(140,346)(141,350)(142,349)(143,351)(144,352)
(145,315)(146,316)(147,313)(148,314)(149,318)(150,317)(151,319)(152,320)
(153,331)(154,332)(155,329)(156,330)(157,334)(158,333)(159,335)(160,336)
(161,323)(162,324)(163,321)(164,322)(165,326)(166,325)(167,327)(168,328)
(169,291)(170,292)(171,289)(172,290)(173,294)(174,293)(175,295)(176,296)
(177,307)(178,308)(179,305)(180,306)(181,310)(182,309)(183,311)(184,312)
(185,299)(186,300)(187,297)(188,298)(189,302)(190,301)(191,303)(192,304);;
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, s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*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*s0*s1*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)( 97,121)( 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)( 49,185)( 50,186)( 51,190)( 52,189)( 53,188)( 54,187)( 55,192)
( 56,191)( 57,177)( 58,178)( 59,182)( 60,181)( 61,180)( 62,179)( 63,184)
( 64,183)( 65,169)( 66,170)( 67,174)( 68,173)( 69,172)( 70,171)( 71,176)
( 72,175)( 73,161)( 74,162)( 75,166)( 76,165)( 77,164)( 78,163)( 79,168)
( 80,167)( 81,153)( 82,154)( 83,158)( 84,157)( 85,156)( 86,155)( 87,160)
( 88,159)( 89,145)( 90,146)( 91,150)( 92,149)( 93,148)( 94,147)( 95,152)
( 96,151)(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)(241,378)(242,377)(243,381)(244,382)(245,379)(246,380)(247,383)
(248,384)(249,370)(250,369)(251,373)(252,374)(253,371)(254,372)(255,375)
(256,376)(257,362)(258,361)(259,365)(260,366)(261,363)(262,364)(263,367)
(264,368)(265,354)(266,353)(267,357)(268,358)(269,355)(270,356)(271,359)
(272,360)(273,346)(274,345)(275,349)(276,350)(277,347)(278,348)(279,351)
(280,352)(281,338)(282,337)(283,341)(284,342)(285,339)(286,340)(287,343)
(288,344);
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)( 49,243)( 50,244)( 51,241)( 52,242)( 53,246)( 54,245)( 55,247)
( 56,248)( 57,259)( 58,260)( 59,257)( 60,258)( 61,262)( 62,261)( 63,263)
( 64,264)( 65,251)( 66,252)( 67,249)( 68,250)( 69,254)( 70,253)( 71,255)
( 72,256)( 73,267)( 74,268)( 75,265)( 76,266)( 77,270)( 78,269)( 79,271)
( 80,272)( 81,283)( 82,284)( 83,281)( 84,282)( 85,286)( 86,285)( 87,287)
( 88,288)( 89,275)( 90,276)( 91,273)( 92,274)( 93,278)( 94,277)( 95,279)
( 96,280)( 97,363)( 98,364)( 99,361)(100,362)(101,366)(102,365)(103,367)
(104,368)(105,379)(106,380)(107,377)(108,378)(109,382)(110,381)(111,383)
(112,384)(113,371)(114,372)(115,369)(116,370)(117,374)(118,373)(119,375)
(120,376)(121,339)(122,340)(123,337)(124,338)(125,342)(126,341)(127,343)
(128,344)(129,355)(130,356)(131,353)(132,354)(133,358)(134,357)(135,359)
(136,360)(137,347)(138,348)(139,345)(140,346)(141,350)(142,349)(143,351)
(144,352)(145,315)(146,316)(147,313)(148,314)(149,318)(150,317)(151,319)
(152,320)(153,331)(154,332)(155,329)(156,330)(157,334)(158,333)(159,335)
(160,336)(161,323)(162,324)(163,321)(164,322)(165,326)(166,325)(167,327)
(168,328)(169,291)(170,292)(171,289)(172,290)(173,294)(174,293)(175,295)
(176,296)(177,307)(178,308)(179,305)(180,306)(181,310)(182,309)(183,311)
(184,312)(185,299)(186,300)(187,297)(188,298)(189,302)(190,301)(191,303)
(192,304);
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, s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*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*s0*s1*s0*s1 >;

References : None.
to this polytope