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Polytope of Type {12,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*768b
if this polytope has a name.
Group : SmallGroup(768,1086909)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 16, 192, 32
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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}*384c, {6,24}*384b
   4-fold quotients : {6,12}*192a, {12,6}*192b
   8-fold quotients : {12,3}*96, {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   32-fold quotients : {3,3}*24
   48-fold quotients : {2,4}*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)( 97,122)( 98,121)( 99,123)(100,124)
(101,128)(102,127)(103,126)(104,125)(105,138)(106,137)(107,139)(108,140)
(109,144)(110,143)(111,142)(112,141)(113,130)(114,129)(115,131)(116,132)
(117,136)(118,135)(119,134)(120,133)(145,170)(146,169)(147,171)(148,172)
(149,176)(150,175)(151,174)(152,173)(153,186)(154,185)(155,187)(156,188)
(157,192)(158,191)(159,190)(160,189)(161,178)(162,177)(163,179)(164,180)
(165,184)(166,183)(167,182)(168,181)(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)
(289,313)(290,314)(291,316)(292,315)(293,319)(294,320)(295,317)(296,318)
(297,329)(298,330)(299,332)(300,331)(301,335)(302,336)(303,333)(304,334)
(305,321)(306,322)(307,324)(308,323)(309,327)(310,328)(311,325)(312,326)
(337,361)(338,362)(339,364)(340,363)(341,367)(342,368)(343,365)(344,366)
(345,377)(346,378)(347,380)(348,379)(349,383)(350,384)(351,381)(352,382)
(353,369)(354,370)(355,372)(356,371)(357,375)(358,376)(359,373)(360,374);;
s1 := (  1,138)(  2,137)(  3,141)(  4,142)(  5,139)(  6,140)(  7,143)(  8,144)
(  9,130)( 10,129)( 11,133)( 12,134)( 13,131)( 14,132)( 15,135)( 16,136)
( 17,122)( 18,121)( 19,125)( 20,126)( 21,123)( 22,124)( 23,127)( 24,128)
( 25,114)( 26,113)( 27,117)( 28,118)( 29,115)( 30,116)( 31,119)( 32,120)
( 33,106)( 34,105)( 35,109)( 36,110)( 37,107)( 38,108)( 39,111)( 40,112)
( 41, 98)( 42, 97)( 43,101)( 44,102)( 45, 99)( 46,100)( 47,103)( 48,104)
( 49,162)( 50,161)( 51,165)( 52,166)( 53,163)( 54,164)( 55,167)( 56,168)
( 57,154)( 58,153)( 59,157)( 60,158)( 61,155)( 62,156)( 63,159)( 64,160)
( 65,146)( 66,145)( 67,149)( 68,150)( 69,147)( 70,148)( 71,151)( 72,152)
( 73,186)( 74,185)( 75,189)( 76,190)( 77,187)( 78,188)( 79,191)( 80,192)
( 81,178)( 82,177)( 83,181)( 84,182)( 85,179)( 86,180)( 87,183)( 88,184)
( 89,170)( 90,169)( 91,173)( 92,174)( 93,171)( 94,172)( 95,175)( 96,176)
(193,329)(194,330)(195,334)(196,333)(197,332)(198,331)(199,336)(200,335)
(201,321)(202,322)(203,326)(204,325)(205,324)(206,323)(207,328)(208,327)
(209,313)(210,314)(211,318)(212,317)(213,316)(214,315)(215,320)(216,319)
(217,305)(218,306)(219,310)(220,309)(221,308)(222,307)(223,312)(224,311)
(225,297)(226,298)(227,302)(228,301)(229,300)(230,299)(231,304)(232,303)
(233,289)(234,290)(235,294)(236,293)(237,292)(238,291)(239,296)(240,295)
(241,353)(242,354)(243,358)(244,357)(245,356)(246,355)(247,360)(248,359)
(249,345)(250,346)(251,350)(252,349)(253,348)(254,347)(255,352)(256,351)
(257,337)(258,338)(259,342)(260,341)(261,340)(262,339)(263,344)(264,343)
(265,377)(266,378)(267,382)(268,381)(269,380)(270,379)(271,384)(272,383)
(273,369)(274,370)(275,374)(276,373)(277,372)(278,371)(279,376)(280,375)
(281,361)(282,362)(283,366)(284,365)(285,364)(286,363)(287,368)(288,367);;
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)
( 49,267)( 50,268)( 51,265)( 52,266)( 53,270)( 54,269)( 55,271)( 56,272)
( 57,283)( 58,284)( 59,281)( 60,282)( 61,286)( 62,285)( 63,287)( 64,288)
( 65,275)( 66,276)( 67,273)( 68,274)( 69,278)( 70,277)( 71,279)( 72,280)
( 73,243)( 74,244)( 75,241)( 76,242)( 77,246)( 78,245)( 79,247)( 80,248)
( 81,259)( 82,260)( 83,257)( 84,258)( 85,262)( 86,261)( 87,263)( 88,264)
( 89,251)( 90,252)( 91,249)( 92,250)( 93,254)( 94,253)( 95,255)( 96,256)
( 97,364)( 98,363)( 99,362)(100,361)(101,365)(102,366)(103,368)(104,367)
(105,380)(106,379)(107,378)(108,377)(109,381)(110,382)(111,384)(112,383)
(113,372)(114,371)(115,370)(116,369)(117,373)(118,374)(119,376)(120,375)
(121,340)(122,339)(123,338)(124,337)(125,341)(126,342)(127,344)(128,343)
(129,356)(130,355)(131,354)(132,353)(133,357)(134,358)(135,360)(136,359)
(137,348)(138,347)(139,346)(140,345)(141,349)(142,350)(143,352)(144,351)
(145,316)(146,315)(147,314)(148,313)(149,317)(150,318)(151,320)(152,319)
(153,332)(154,331)(155,330)(156,329)(157,333)(158,334)(159,336)(160,335)
(161,324)(162,323)(163,322)(164,321)(165,325)(166,326)(167,328)(168,327)
(169,292)(170,291)(171,290)(172,289)(173,293)(174,294)(175,296)(176,295)
(177,308)(178,307)(179,306)(180,305)(181,309)(182,310)(183,312)(184,311)
(185,300)(186,299)(187,298)(188,297)(189,301)(190,302)(191,304)(192,303);;
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*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*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)( 97,122)( 98,121)( 99,123)
(100,124)(101,128)(102,127)(103,126)(104,125)(105,138)(106,137)(107,139)
(108,140)(109,144)(110,143)(111,142)(112,141)(113,130)(114,129)(115,131)
(116,132)(117,136)(118,135)(119,134)(120,133)(145,170)(146,169)(147,171)
(148,172)(149,176)(150,175)(151,174)(152,173)(153,186)(154,185)(155,187)
(156,188)(157,192)(158,191)(159,190)(160,189)(161,178)(162,177)(163,179)
(164,180)(165,184)(166,183)(167,182)(168,181)(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)(289,313)(290,314)(291,316)(292,315)(293,319)(294,320)(295,317)
(296,318)(297,329)(298,330)(299,332)(300,331)(301,335)(302,336)(303,333)
(304,334)(305,321)(306,322)(307,324)(308,323)(309,327)(310,328)(311,325)
(312,326)(337,361)(338,362)(339,364)(340,363)(341,367)(342,368)(343,365)
(344,366)(345,377)(346,378)(347,380)(348,379)(349,383)(350,384)(351,381)
(352,382)(353,369)(354,370)(355,372)(356,371)(357,375)(358,376)(359,373)
(360,374);
s1 := Sym(384)!(  1,138)(  2,137)(  3,141)(  4,142)(  5,139)(  6,140)(  7,143)
(  8,144)(  9,130)( 10,129)( 11,133)( 12,134)( 13,131)( 14,132)( 15,135)
( 16,136)( 17,122)( 18,121)( 19,125)( 20,126)( 21,123)( 22,124)( 23,127)
( 24,128)( 25,114)( 26,113)( 27,117)( 28,118)( 29,115)( 30,116)( 31,119)
( 32,120)( 33,106)( 34,105)( 35,109)( 36,110)( 37,107)( 38,108)( 39,111)
( 40,112)( 41, 98)( 42, 97)( 43,101)( 44,102)( 45, 99)( 46,100)( 47,103)
( 48,104)( 49,162)( 50,161)( 51,165)( 52,166)( 53,163)( 54,164)( 55,167)
( 56,168)( 57,154)( 58,153)( 59,157)( 60,158)( 61,155)( 62,156)( 63,159)
( 64,160)( 65,146)( 66,145)( 67,149)( 68,150)( 69,147)( 70,148)( 71,151)
( 72,152)( 73,186)( 74,185)( 75,189)( 76,190)( 77,187)( 78,188)( 79,191)
( 80,192)( 81,178)( 82,177)( 83,181)( 84,182)( 85,179)( 86,180)( 87,183)
( 88,184)( 89,170)( 90,169)( 91,173)( 92,174)( 93,171)( 94,172)( 95,175)
( 96,176)(193,329)(194,330)(195,334)(196,333)(197,332)(198,331)(199,336)
(200,335)(201,321)(202,322)(203,326)(204,325)(205,324)(206,323)(207,328)
(208,327)(209,313)(210,314)(211,318)(212,317)(213,316)(214,315)(215,320)
(216,319)(217,305)(218,306)(219,310)(220,309)(221,308)(222,307)(223,312)
(224,311)(225,297)(226,298)(227,302)(228,301)(229,300)(230,299)(231,304)
(232,303)(233,289)(234,290)(235,294)(236,293)(237,292)(238,291)(239,296)
(240,295)(241,353)(242,354)(243,358)(244,357)(245,356)(246,355)(247,360)
(248,359)(249,345)(250,346)(251,350)(252,349)(253,348)(254,347)(255,352)
(256,351)(257,337)(258,338)(259,342)(260,341)(261,340)(262,339)(263,344)
(264,343)(265,377)(266,378)(267,382)(268,381)(269,380)(270,379)(271,384)
(272,383)(273,369)(274,370)(275,374)(276,373)(277,372)(278,371)(279,376)
(280,375)(281,361)(282,362)(283,366)(284,365)(285,364)(286,363)(287,368)
(288,367);
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)( 49,267)( 50,268)( 51,265)( 52,266)( 53,270)( 54,269)( 55,271)
( 56,272)( 57,283)( 58,284)( 59,281)( 60,282)( 61,286)( 62,285)( 63,287)
( 64,288)( 65,275)( 66,276)( 67,273)( 68,274)( 69,278)( 70,277)( 71,279)
( 72,280)( 73,243)( 74,244)( 75,241)( 76,242)( 77,246)( 78,245)( 79,247)
( 80,248)( 81,259)( 82,260)( 83,257)( 84,258)( 85,262)( 86,261)( 87,263)
( 88,264)( 89,251)( 90,252)( 91,249)( 92,250)( 93,254)( 94,253)( 95,255)
( 96,256)( 97,364)( 98,363)( 99,362)(100,361)(101,365)(102,366)(103,368)
(104,367)(105,380)(106,379)(107,378)(108,377)(109,381)(110,382)(111,384)
(112,383)(113,372)(114,371)(115,370)(116,369)(117,373)(118,374)(119,376)
(120,375)(121,340)(122,339)(123,338)(124,337)(125,341)(126,342)(127,344)
(128,343)(129,356)(130,355)(131,354)(132,353)(133,357)(134,358)(135,360)
(136,359)(137,348)(138,347)(139,346)(140,345)(141,349)(142,350)(143,352)
(144,351)(145,316)(146,315)(147,314)(148,313)(149,317)(150,318)(151,320)
(152,319)(153,332)(154,331)(155,330)(156,329)(157,333)(158,334)(159,336)
(160,335)(161,324)(162,323)(163,322)(164,321)(165,325)(166,326)(167,328)
(168,327)(169,292)(170,291)(171,290)(172,289)(173,293)(174,294)(175,296)
(176,295)(177,308)(178,307)(179,306)(180,305)(181,309)(182,310)(183,312)
(184,311)(185,300)(186,299)(187,298)(188,297)(189,301)(190,302)(191,304)
(192,303);
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*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1 >; 
 
References : None.
to this polytope