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Polytope of Type {24,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,16}*768f
if this polytope has a name.
Group : SmallGroup(768,83051)
Rank : 3
Schlafli Type : {24,16}
Number of vertices, edges, etc : 24, 192, 16
Order of s0s1s2 : 48
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 : {24,8}*384b, {12,16}*384b
   3-fold quotients : {8,16}*256f
   4-fold quotients : {24,4}*192a, {12,8}*192a
   6-fold quotients : {8,8}*128b, {4,16}*128b
   8-fold quotients : {12,4}*96a, {24,2}*96, {6,8}*96
   12-fold quotients : {4,8}*64a, {8,4}*64a
   16-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {4,4}*32, {2,8}*32, {8,2}*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)
( 25,130)( 26,132)( 27,131)( 28,127)( 29,129)( 30,128)( 31,124)( 32,126)
( 33,125)( 34,121)( 35,123)( 36,122)( 37,142)( 38,144)( 39,143)( 40,139)
( 41,141)( 42,140)( 43,136)( 44,138)( 45,137)( 46,133)( 47,135)( 48,134)
( 49,151)( 50,153)( 51,152)( 52,154)( 53,156)( 54,155)( 55,145)( 56,147)
( 57,146)( 58,148)( 59,150)( 60,149)( 61,163)( 62,165)( 63,164)( 64,166)
( 65,168)( 66,167)( 67,157)( 68,159)( 69,158)( 70,160)( 71,162)( 72,161)
( 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)
(217,322)(218,324)(219,323)(220,319)(221,321)(222,320)(223,316)(224,318)
(225,317)(226,313)(227,315)(228,314)(229,334)(230,336)(231,335)(232,331)
(233,333)(234,332)(235,328)(236,330)(237,329)(238,325)(239,327)(240,326)
(241,343)(242,345)(243,344)(244,346)(245,348)(246,347)(247,337)(248,339)
(249,338)(250,340)(251,342)(252,341)(253,355)(254,357)(255,356)(256,358)
(257,360)(258,359)(259,349)(260,351)(261,350)(262,352)(263,354)(264,353)
(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,  9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)( 19, 24)
( 20, 23)( 21, 22)( 25, 36)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)
( 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, 69)( 56, 68)( 57, 67)( 58, 72)
( 59, 71)( 60, 70)( 73, 96)( 74, 95)( 75, 94)( 76, 93)( 77, 92)( 78, 91)
( 79, 90)( 80, 89)( 81, 88)( 82, 87)( 83, 86)( 84, 85)( 97,123)( 98,122)
( 99,121)(100,126)(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)
(107,131)(108,130)(109,138)(110,137)(111,136)(112,135)(113,134)(114,133)
(115,144)(116,143)(117,142)(118,141)(119,140)(120,139)(145,183)(146,182)
(147,181)(148,186)(149,185)(150,184)(151,189)(152,188)(153,187)(154,192)
(155,191)(156,190)(157,171)(158,170)(159,169)(160,174)(161,173)(162,172)
(163,177)(164,176)(165,175)(166,180)(167,179)(168,178)(193,243)(194,242)
(195,241)(196,246)(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)
(203,251)(204,250)(205,258)(206,257)(207,256)(208,255)(209,254)(210,253)
(211,264)(212,263)(213,262)(214,261)(215,260)(216,259)(217,276)(218,275)
(219,274)(220,273)(221,272)(222,271)(223,270)(224,269)(225,268)(226,267)
(227,266)(228,265)(229,285)(230,284)(231,283)(232,288)(233,287)(234,286)
(235,279)(236,278)(237,277)(238,282)(239,281)(240,280)(289,369)(290,368)
(291,367)(292,372)(293,371)(294,370)(295,363)(296,362)(297,361)(298,366)
(299,365)(300,364)(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)
(307,378)(308,377)(309,376)(310,375)(311,374)(312,373)(313,345)(314,344)
(315,343)(316,348)(317,347)(318,346)(319,339)(320,338)(321,337)(322,342)
(323,341)(324,340)(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 := (  1,289)(  2,290)(  3,291)(  4,292)(  5,293)(  6,294)(  7,295)(  8,296)
(  9,297)( 10,298)( 11,299)( 12,300)( 13,304)( 14,305)( 15,306)( 16,301)
( 17,302)( 18,303)( 19,310)( 20,311)( 21,312)( 22,307)( 23,308)( 24,309)
( 25,316)( 26,317)( 27,318)( 28,313)( 29,314)( 30,315)( 31,322)( 32,323)
( 33,324)( 34,319)( 35,320)( 36,321)( 37,325)( 38,326)( 39,327)( 40,328)
( 41,329)( 42,330)( 43,331)( 44,332)( 45,333)( 46,334)( 47,335)( 48,336)
( 49,355)( 50,356)( 51,357)( 52,358)( 53,359)( 54,360)( 55,349)( 56,350)
( 57,351)( 58,352)( 59,353)( 60,354)( 61,343)( 62,344)( 63,345)( 64,346)
( 65,347)( 66,348)( 67,337)( 68,338)( 69,339)( 70,340)( 71,341)( 72,342)
( 73,382)( 74,383)( 75,384)( 76,379)( 77,380)( 78,381)( 79,376)( 80,377)
( 81,378)( 82,373)( 83,374)( 84,375)( 85,370)( 86,371)( 87,372)( 88,367)
( 89,368)( 90,369)( 91,364)( 92,365)( 93,366)( 94,361)( 95,362)( 96,363)
( 97,193)( 98,194)( 99,195)(100,196)(101,197)(102,198)(103,199)(104,200)
(105,201)(106,202)(107,203)(108,204)(109,208)(110,209)(111,210)(112,205)
(113,206)(114,207)(115,214)(116,215)(117,216)(118,211)(119,212)(120,213)
(121,220)(122,221)(123,222)(124,217)(125,218)(126,219)(127,226)(128,227)
(129,228)(130,223)(131,224)(132,225)(133,229)(134,230)(135,231)(136,232)
(137,233)(138,234)(139,235)(140,236)(141,237)(142,238)(143,239)(144,240)
(145,259)(146,260)(147,261)(148,262)(149,263)(150,264)(151,253)(152,254)
(153,255)(154,256)(155,257)(156,258)(157,247)(158,248)(159,249)(160,250)
(161,251)(162,252)(163,241)(164,242)(165,243)(166,244)(167,245)(168,246)
(169,286)(170,287)(171,288)(172,283)(173,284)(174,285)(175,280)(176,281)
(177,282)(178,277)(179,278)(180,279)(181,274)(182,275)(183,276)(184,271)
(185,272)(186,273)(187,268)(188,269)(189,270)(190,265)(191,266)(192,267);;
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, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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, 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)( 25,130)( 26,132)( 27,131)( 28,127)( 29,129)( 30,128)( 31,124)
( 32,126)( 33,125)( 34,121)( 35,123)( 36,122)( 37,142)( 38,144)( 39,143)
( 40,139)( 41,141)( 42,140)( 43,136)( 44,138)( 45,137)( 46,133)( 47,135)
( 48,134)( 49,151)( 50,153)( 51,152)( 52,154)( 53,156)( 54,155)( 55,145)
( 56,147)( 57,146)( 58,148)( 59,150)( 60,149)( 61,163)( 62,165)( 63,164)
( 64,166)( 65,168)( 66,167)( 67,157)( 68,159)( 69,158)( 70,160)( 71,162)
( 72,161)( 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)(217,322)(218,324)(219,323)(220,319)(221,321)(222,320)(223,316)
(224,318)(225,317)(226,313)(227,315)(228,314)(229,334)(230,336)(231,335)
(232,331)(233,333)(234,332)(235,328)(236,330)(237,329)(238,325)(239,327)
(240,326)(241,343)(242,345)(243,344)(244,346)(245,348)(246,347)(247,337)
(248,339)(249,338)(250,340)(251,342)(252,341)(253,355)(254,357)(255,356)
(256,358)(257,360)(258,359)(259,349)(260,351)(261,350)(262,352)(263,354)
(264,353)(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,  9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)
( 19, 24)( 20, 23)( 21, 22)( 25, 36)( 26, 35)( 27, 34)( 28, 33)( 29, 32)
( 30, 31)( 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, 69)( 56, 68)( 57, 67)
( 58, 72)( 59, 71)( 60, 70)( 73, 96)( 74, 95)( 75, 94)( 76, 93)( 77, 92)
( 78, 91)( 79, 90)( 80, 89)( 81, 88)( 82, 87)( 83, 86)( 84, 85)( 97,123)
( 98,122)( 99,121)(100,126)(101,125)(102,124)(103,129)(104,128)(105,127)
(106,132)(107,131)(108,130)(109,138)(110,137)(111,136)(112,135)(113,134)
(114,133)(115,144)(116,143)(117,142)(118,141)(119,140)(120,139)(145,183)
(146,182)(147,181)(148,186)(149,185)(150,184)(151,189)(152,188)(153,187)
(154,192)(155,191)(156,190)(157,171)(158,170)(159,169)(160,174)(161,173)
(162,172)(163,177)(164,176)(165,175)(166,180)(167,179)(168,178)(193,243)
(194,242)(195,241)(196,246)(197,245)(198,244)(199,249)(200,248)(201,247)
(202,252)(203,251)(204,250)(205,258)(206,257)(207,256)(208,255)(209,254)
(210,253)(211,264)(212,263)(213,262)(214,261)(215,260)(216,259)(217,276)
(218,275)(219,274)(220,273)(221,272)(222,271)(223,270)(224,269)(225,268)
(226,267)(227,266)(228,265)(229,285)(230,284)(231,283)(232,288)(233,287)
(234,286)(235,279)(236,278)(237,277)(238,282)(239,281)(240,280)(289,369)
(290,368)(291,367)(292,372)(293,371)(294,370)(295,363)(296,362)(297,361)
(298,366)(299,365)(300,364)(301,384)(302,383)(303,382)(304,381)(305,380)
(306,379)(307,378)(308,377)(309,376)(310,375)(311,374)(312,373)(313,345)
(314,344)(315,343)(316,348)(317,347)(318,346)(319,339)(320,338)(321,337)
(322,342)(323,341)(324,340)(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)!(  1,289)(  2,290)(  3,291)(  4,292)(  5,293)(  6,294)(  7,295)
(  8,296)(  9,297)( 10,298)( 11,299)( 12,300)( 13,304)( 14,305)( 15,306)
( 16,301)( 17,302)( 18,303)( 19,310)( 20,311)( 21,312)( 22,307)( 23,308)
( 24,309)( 25,316)( 26,317)( 27,318)( 28,313)( 29,314)( 30,315)( 31,322)
( 32,323)( 33,324)( 34,319)( 35,320)( 36,321)( 37,325)( 38,326)( 39,327)
( 40,328)( 41,329)( 42,330)( 43,331)( 44,332)( 45,333)( 46,334)( 47,335)
( 48,336)( 49,355)( 50,356)( 51,357)( 52,358)( 53,359)( 54,360)( 55,349)
( 56,350)( 57,351)( 58,352)( 59,353)( 60,354)( 61,343)( 62,344)( 63,345)
( 64,346)( 65,347)( 66,348)( 67,337)( 68,338)( 69,339)( 70,340)( 71,341)
( 72,342)( 73,382)( 74,383)( 75,384)( 76,379)( 77,380)( 78,381)( 79,376)
( 80,377)( 81,378)( 82,373)( 83,374)( 84,375)( 85,370)( 86,371)( 87,372)
( 88,367)( 89,368)( 90,369)( 91,364)( 92,365)( 93,366)( 94,361)( 95,362)
( 96,363)( 97,193)( 98,194)( 99,195)(100,196)(101,197)(102,198)(103,199)
(104,200)(105,201)(106,202)(107,203)(108,204)(109,208)(110,209)(111,210)
(112,205)(113,206)(114,207)(115,214)(116,215)(117,216)(118,211)(119,212)
(120,213)(121,220)(122,221)(123,222)(124,217)(125,218)(126,219)(127,226)
(128,227)(129,228)(130,223)(131,224)(132,225)(133,229)(134,230)(135,231)
(136,232)(137,233)(138,234)(139,235)(140,236)(141,237)(142,238)(143,239)
(144,240)(145,259)(146,260)(147,261)(148,262)(149,263)(150,264)(151,253)
(152,254)(153,255)(154,256)(155,257)(156,258)(157,247)(158,248)(159,249)
(160,250)(161,251)(162,252)(163,241)(164,242)(165,243)(166,244)(167,245)
(168,246)(169,286)(170,287)(171,288)(172,283)(173,284)(174,285)(175,280)
(176,281)(177,282)(178,277)(179,278)(180,279)(181,274)(182,275)(183,276)
(184,271)(185,272)(186,273)(187,268)(188,269)(189,270)(190,265)(191,266)
(192,267);
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, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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