Polytope of Type {4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12}*768h
if this polytope has a name.
Group : SmallGroup(768,1088561)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 32, 192, 96
Order of s₀s₁s₂ : 12
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 : {4,6}*384a
   4-fold quotients : {4,6}*192a
   8-fold quotients : {4,6}*96
   16-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {4,3}*24, {2,6}*24
   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 := (  1,221)(  2,222)(  3,224)(  4,223)(  5,218)(  6,217)(  7,219)(  8,220)
(  9,213)( 10,214)( 11,216)( 12,215)( 13,210)( 14,209)( 15,211)( 16,212)
( 17,205)( 18,206)( 19,208)( 20,207)( 21,202)( 22,201)( 23,203)( 24,204)
( 25,197)( 26,198)( 27,200)( 28,199)( 29,194)( 30,193)( 31,195)( 32,196)
( 33,253)( 34,254)( 35,256)( 36,255)( 37,250)( 38,249)( 39,251)( 40,252)
( 41,245)( 42,246)( 43,248)( 44,247)( 45,242)( 46,241)( 47,243)( 48,244)
( 49,237)( 50,238)( 51,240)( 52,239)( 53,234)( 54,233)( 55,235)( 56,236)
( 57,229)( 58,230)( 59,232)( 60,231)( 61,226)( 62,225)( 63,227)( 64,228)
( 65,285)( 66,286)( 67,288)( 68,287)( 69,282)( 70,281)( 71,283)( 72,284)
( 73,277)( 74,278)( 75,280)( 76,279)( 77,274)( 78,273)( 79,275)( 80,276)
( 81,269)( 82,270)( 83,272)( 84,271)( 85,266)( 86,265)( 87,267)( 88,268)
( 89,261)( 90,262)( 91,264)( 92,263)( 93,258)( 94,257)( 95,259)( 96,260)
( 97,318)( 98,317)( 99,319)(100,320)(101,313)(102,314)(103,316)(104,315)
(105,310)(106,309)(107,311)(108,312)(109,305)(110,306)(111,308)(112,307)
(113,302)(114,301)(115,303)(116,304)(117,297)(118,298)(119,300)(120,299)
(121,294)(122,293)(123,295)(124,296)(125,289)(126,290)(127,292)(128,291)
(129,350)(130,349)(131,351)(132,352)(133,345)(134,346)(135,348)(136,347)
(137,342)(138,341)(139,343)(140,344)(141,337)(142,338)(143,340)(144,339)
(145,334)(146,333)(147,335)(148,336)(149,329)(150,330)(151,332)(152,331)
(153,326)(154,325)(155,327)(156,328)(157,321)(158,322)(159,324)(160,323)
(161,382)(162,381)(163,383)(164,384)(165,377)(166,378)(167,380)(168,379)
(169,374)(170,373)(171,375)(172,376)(173,369)(174,370)(175,372)(176,371)
(177,366)(178,365)(179,367)(180,368)(181,361)(182,362)(183,364)(184,363)
(185,358)(186,357)(187,359)(188,360)(189,353)(190,354)(191,356)(192,355);;
s1 := (  5,  7)(  6,  8)( 13, 15)( 14, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)
( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 33, 65)( 34, 66)( 35, 67)( 36, 68)
( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 73)( 42, 74)( 43, 75)( 44, 76)
( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 89)( 50, 90)( 51, 91)( 52, 92)
( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)( 58, 82)( 59, 83)( 60, 84)
( 61, 87)( 62, 88)( 63, 85)( 64, 86)( 97, 98)( 99,100)(101,104)(102,103)
(105,106)(107,108)(109,112)(110,111)(113,122)(114,121)(115,124)(116,123)
(117,128)(118,127)(119,126)(120,125)(129,162)(130,161)(131,164)(132,163)
(133,168)(134,167)(135,166)(136,165)(137,170)(138,169)(139,172)(140,171)
(141,176)(142,175)(143,174)(144,173)(145,186)(146,185)(147,188)(148,187)
(149,192)(150,191)(151,190)(152,189)(153,178)(154,177)(155,180)(156,179)
(157,184)(158,183)(159,182)(160,181)(197,199)(198,200)(205,207)(206,208)
(209,217)(210,218)(211,219)(212,220)(213,223)(214,224)(215,221)(216,222)
(225,257)(226,258)(227,259)(228,260)(229,263)(230,264)(231,261)(232,262)
(233,265)(234,266)(235,267)(236,268)(237,271)(238,272)(239,269)(240,270)
(241,281)(242,282)(243,283)(244,284)(245,287)(246,288)(247,285)(248,286)
(249,273)(250,274)(251,275)(252,276)(253,279)(254,280)(255,277)(256,278)
(289,290)(291,292)(293,296)(294,295)(297,298)(299,300)(301,304)(302,303)
(305,314)(306,313)(307,316)(308,315)(309,320)(310,319)(311,318)(312,317)
(321,354)(322,353)(323,356)(324,355)(325,360)(326,359)(327,358)(328,357)
(329,362)(330,361)(331,364)(332,363)(333,368)(334,367)(335,366)(336,365)
(337,378)(338,377)(339,380)(340,379)(341,384)(342,383)(343,382)(344,381)
(345,370)(346,369)(347,372)(348,371)(349,376)(350,375)(351,374)(352,373);;
s2 := (  1,162)(  2,161)(  3,166)(  4,165)(  5,164)(  6,163)(  7,168)(  8,167)
(  9,181)( 10,182)( 11,177)( 12,178)( 13,183)( 14,184)( 15,179)( 16,180)
( 17,171)( 18,172)( 19,175)( 20,176)( 21,169)( 22,170)( 23,173)( 24,174)
( 25,191)( 26,192)( 27,187)( 28,188)( 29,189)( 30,190)( 31,185)( 32,186)
( 33,130)( 34,129)( 35,134)( 36,133)( 37,132)( 38,131)( 39,136)( 40,135)
( 41,149)( 42,150)( 43,145)( 44,146)( 45,151)( 46,152)( 47,147)( 48,148)
( 49,139)( 50,140)( 51,143)( 52,144)( 53,137)( 54,138)( 55,141)( 56,142)
( 57,159)( 58,160)( 59,155)( 60,156)( 61,157)( 62,158)( 63,153)( 64,154)
( 65, 98)( 66, 97)( 67,102)( 68,101)( 69,100)( 70, 99)( 71,104)( 72,103)
( 73,117)( 74,118)( 75,113)( 76,114)( 77,119)( 78,120)( 79,115)( 80,116)
( 81,107)( 82,108)( 83,111)( 84,112)( 85,105)( 86,106)( 87,109)( 88,110)
( 89,127)( 90,128)( 91,123)( 92,124)( 93,125)( 94,126)( 95,121)( 96,122)
(193,354)(194,353)(195,358)(196,357)(197,356)(198,355)(199,360)(200,359)
(201,373)(202,374)(203,369)(204,370)(205,375)(206,376)(207,371)(208,372)
(209,363)(210,364)(211,367)(212,368)(213,361)(214,362)(215,365)(216,366)
(217,383)(218,384)(219,379)(220,380)(221,381)(222,382)(223,377)(224,378)
(225,322)(226,321)(227,326)(228,325)(229,324)(230,323)(231,328)(232,327)
(233,341)(234,342)(235,337)(236,338)(237,343)(238,344)(239,339)(240,340)
(241,331)(242,332)(243,335)(244,336)(245,329)(246,330)(247,333)(248,334)
(249,351)(250,352)(251,347)(252,348)(253,349)(254,350)(255,345)(256,346)
(257,290)(258,289)(259,294)(260,293)(261,292)(262,291)(263,296)(264,295)
(265,309)(266,310)(267,305)(268,306)(269,311)(270,312)(271,307)(272,308)
(273,299)(274,300)(275,303)(276,304)(277,297)(278,298)(279,301)(280,302)
(281,319)(282,320)(283,315)(284,316)(285,317)(286,318)(287,313)(288,314);;
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, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s0 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope