Polytope of Type {12,32}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,32}*768b
if this polytope has a name.
Group : SmallGroup(768,90242)
Rank : 3
Schlafli Type : {12,32}
Number of vertices, edges, etc : 12, 192, 32
Order of s₀s₁s₂ : 96
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {12,16}*384a
   3-fold quotients : {4,32}*256b
   4-fold quotients : {12,8}*192a, {6,16}*192
   6-fold quotients : {4,16}*128a
   8-fold quotients : {12,4}*96a, {6,8}*96
   12-fold quotients : {4,8}*64a, {2,16}*64
   16-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {4,4}*32, {2,8}*32
   32-fold quotients : {6,2}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   64-fold quotients : {3,2}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope