Polytope of Type {32,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,12}*768b
if this polytope has a name.
Group : SmallGroup(768,90242)
Rank : 3
Schlafli Type : {32,12}
Number of vertices, edges, etc : 32, 192, 12
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 : {16,12}*384a
   3-fold quotients : {32,4}*256b
   4-fold quotients : {8,12}*192a, {16,6}*192
   6-fold quotients : {16,4}*128a
   8-fold quotients : {4,12}*96a, {8,6}*96
   12-fold quotients : {8,4}*64a, {16,2}*64
   16-fold quotients : {2,12}*48, {4,6}*48a
   24-fold quotients : {4,4}*32, {8,2}*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.
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)( 13,211)( 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);;
s1 := (  2,  3)(  5,  6)(  7, 10)(  8, 12)(  9, 11)( 13, 19)( 14, 21)( 15, 20)
( 16, 22)( 17, 24)( 18, 23)( 26, 27)( 29, 30)( 31, 34)( 32, 36)( 33, 35)
( 37, 43)( 38, 45)( 39, 44)( 40, 46)( 41, 48)( 42, 47)( 49, 61)( 50, 63)
( 51, 62)( 52, 64)( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)( 58, 67)
( 59, 69)( 60, 68)( 73, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 90)( 78, 89)
( 79, 94)( 80, 96)( 81, 95)( 82, 91)( 83, 93)( 84, 92)( 97,121)( 98,123)
( 99,122)(100,124)(101,126)(102,125)(103,130)(104,132)(105,131)(106,127)
(107,129)(108,128)(109,139)(110,141)(111,140)(112,142)(113,144)(114,143)
(115,133)(116,135)(117,134)(118,136)(119,138)(120,137)(145,181)(146,183)
(147,182)(148,184)(149,186)(150,185)(151,190)(152,192)(153,191)(154,187)
(155,189)(156,188)(157,169)(158,171)(159,170)(160,172)(161,174)(162,173)
(163,178)(164,180)(165,179)(166,175)(167,177)(168,176)(193,241)(194,243)
(195,242)(196,244)(197,246)(198,245)(199,250)(200,252)(201,251)(202,247)
(203,249)(204,248)(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)(223,274)(224,276)(225,275)(226,271)
(227,273)(228,272)(229,283)(230,285)(231,284)(232,286)(233,288)(234,287)
(235,277)(236,279)(237,278)(238,280)(239,282)(240,281)(289,364)(290,366)
(291,365)(292,361)(293,363)(294,362)(295,367)(296,369)(297,368)(298,370)
(299,372)(300,371)(301,382)(302,384)(303,383)(304,379)(305,381)(306,380)
(307,376)(308,378)(309,377)(310,373)(311,375)(312,374)(313,340)(314,342)
(315,341)(316,337)(317,339)(318,338)(319,343)(320,345)(321,344)(322,346)
(323,348)(324,347)(325,358)(326,360)(327,359)(328,355)(329,357)(330,356)
(331,352)(332,354)(333,353)(334,349)(335,351)(336,350);;
s2 := (  1, 99)(  2, 98)(  3, 97)(  4,102)(  5,101)(  6,100)(  7,105)(  8,104)
(  9,103)( 10,108)( 11,107)( 12,106)( 13,111)( 14,110)( 15,109)( 16,114)
( 17,113)( 18,112)( 19,117)( 20,116)( 21,115)( 22,120)( 23,119)( 24,118)
( 25,123)( 26,122)( 27,121)( 28,126)( 29,125)( 30,124)( 31,129)( 32,128)
( 33,127)( 34,132)( 35,131)( 36,130)( 37,135)( 38,134)( 39,133)( 40,138)
( 41,137)( 42,136)( 43,141)( 44,140)( 45,139)( 46,144)( 47,143)( 48,142)
( 49,150)( 50,149)( 51,148)( 52,147)( 53,146)( 54,145)( 55,156)( 56,155)
( 57,154)( 58,153)( 59,152)( 60,151)( 61,162)( 62,161)( 63,160)( 64,159)
( 65,158)( 66,157)( 67,168)( 68,167)( 69,166)( 70,165)( 71,164)( 72,163)
( 73,174)( 74,173)( 75,172)( 76,171)( 77,170)( 78,169)( 79,180)( 80,179)
( 81,178)( 82,177)( 83,176)( 84,175)( 85,186)( 86,185)( 87,184)( 88,183)
( 89,182)( 90,181)( 91,192)( 92,191)( 93,190)( 94,189)( 95,188)( 96,187)
(193,291)(194,290)(195,289)(196,294)(197,293)(198,292)(199,297)(200,296)
(201,295)(202,300)(203,299)(204,298)(205,303)(206,302)(207,301)(208,306)
(209,305)(210,304)(211,309)(212,308)(213,307)(214,312)(215,311)(216,310)
(217,315)(218,314)(219,313)(220,318)(221,317)(222,316)(223,321)(224,320)
(225,319)(226,324)(227,323)(228,322)(229,327)(230,326)(231,325)(232,330)
(233,329)(234,328)(235,333)(236,332)(237,331)(238,336)(239,335)(240,334)
(241,342)(242,341)(243,340)(244,339)(245,338)(246,337)(247,348)(248,347)
(249,346)(250,345)(251,344)(252,343)(253,354)(254,353)(255,352)(256,351)
(257,350)(258,349)(259,360)(260,359)(261,358)(262,357)(263,356)(264,355)
(265,366)(266,365)(267,364)(268,363)(269,362)(270,361)(271,372)(272,371)
(273,370)(274,369)(275,368)(276,367)(277,378)(278,377)(279,376)(280,375)
(281,374)(282,373)(283,384)(284,383)(285,382)(286,381)(287,380)(288,379);;
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, 
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*s0*s2*s1*s0*s1*s0*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 ];;
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)( 13,211)( 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);
s1 := Sym(384)!(  2,  3)(  5,  6)(  7, 10)(  8, 12)(  9, 11)( 13, 19)( 14, 21)
( 15, 20)( 16, 22)( 17, 24)( 18, 23)( 26, 27)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 37, 43)( 38, 45)( 39, 44)( 40, 46)( 41, 48)( 42, 47)( 49, 61)
( 50, 63)( 51, 62)( 52, 64)( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)
( 58, 67)( 59, 69)( 60, 68)( 73, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 90)
( 78, 89)( 79, 94)( 80, 96)( 81, 95)( 82, 91)( 83, 93)( 84, 92)( 97,121)
( 98,123)( 99,122)(100,124)(101,126)(102,125)(103,130)(104,132)(105,131)
(106,127)(107,129)(108,128)(109,139)(110,141)(111,140)(112,142)(113,144)
(114,143)(115,133)(116,135)(117,134)(118,136)(119,138)(120,137)(145,181)
(146,183)(147,182)(148,184)(149,186)(150,185)(151,190)(152,192)(153,191)
(154,187)(155,189)(156,188)(157,169)(158,171)(159,170)(160,172)(161,174)
(162,173)(163,178)(164,180)(165,179)(166,175)(167,177)(168,176)(193,241)
(194,243)(195,242)(196,244)(197,246)(198,245)(199,250)(200,252)(201,251)
(202,247)(203,249)(204,248)(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)(223,274)(224,276)(225,275)
(226,271)(227,273)(228,272)(229,283)(230,285)(231,284)(232,286)(233,288)
(234,287)(235,277)(236,279)(237,278)(238,280)(239,282)(240,281)(289,364)
(290,366)(291,365)(292,361)(293,363)(294,362)(295,367)(296,369)(297,368)
(298,370)(299,372)(300,371)(301,382)(302,384)(303,383)(304,379)(305,381)
(306,380)(307,376)(308,378)(309,377)(310,373)(311,375)(312,374)(313,340)
(314,342)(315,341)(316,337)(317,339)(318,338)(319,343)(320,345)(321,344)
(322,346)(323,348)(324,347)(325,358)(326,360)(327,359)(328,355)(329,357)
(330,356)(331,352)(332,354)(333,353)(334,349)(335,351)(336,350);
s2 := Sym(384)!(  1, 99)(  2, 98)(  3, 97)(  4,102)(  5,101)(  6,100)(  7,105)
(  8,104)(  9,103)( 10,108)( 11,107)( 12,106)( 13,111)( 14,110)( 15,109)
( 16,114)( 17,113)( 18,112)( 19,117)( 20,116)( 21,115)( 22,120)( 23,119)
( 24,118)( 25,123)( 26,122)( 27,121)( 28,126)( 29,125)( 30,124)( 31,129)
( 32,128)( 33,127)( 34,132)( 35,131)( 36,130)( 37,135)( 38,134)( 39,133)
( 40,138)( 41,137)( 42,136)( 43,141)( 44,140)( 45,139)( 46,144)( 47,143)
( 48,142)( 49,150)( 50,149)( 51,148)( 52,147)( 53,146)( 54,145)( 55,156)
( 56,155)( 57,154)( 58,153)( 59,152)( 60,151)( 61,162)( 62,161)( 63,160)
( 64,159)( 65,158)( 66,157)( 67,168)( 68,167)( 69,166)( 70,165)( 71,164)
( 72,163)( 73,174)( 74,173)( 75,172)( 76,171)( 77,170)( 78,169)( 79,180)
( 80,179)( 81,178)( 82,177)( 83,176)( 84,175)( 85,186)( 86,185)( 87,184)
( 88,183)( 89,182)( 90,181)( 91,192)( 92,191)( 93,190)( 94,189)( 95,188)
( 96,187)(193,291)(194,290)(195,289)(196,294)(197,293)(198,292)(199,297)
(200,296)(201,295)(202,300)(203,299)(204,298)(205,303)(206,302)(207,301)
(208,306)(209,305)(210,304)(211,309)(212,308)(213,307)(214,312)(215,311)
(216,310)(217,315)(218,314)(219,313)(220,318)(221,317)(222,316)(223,321)
(224,320)(225,319)(226,324)(227,323)(228,322)(229,327)(230,326)(231,325)
(232,330)(233,329)(234,328)(235,333)(236,332)(237,331)(238,336)(239,335)
(240,334)(241,342)(242,341)(243,340)(244,339)(245,338)(246,337)(247,348)
(248,347)(249,346)(250,345)(251,344)(252,343)(253,354)(254,353)(255,352)
(256,351)(257,350)(258,349)(259,360)(260,359)(261,358)(262,357)(263,356)
(264,355)(265,366)(266,365)(267,364)(268,363)(269,362)(270,361)(271,372)
(272,371)(273,370)(274,369)(275,368)(276,367)(277,378)(278,377)(279,376)
(280,375)(281,374)(282,373)(283,384)(284,383)(285,382)(286,381)(287,380)
(288,379);
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, 
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*s0*s2*s1*s0*s1*s0*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 >;

References : None.
to this polytope