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Polytope of Type {4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*768k
if this polytope has a name.
Group : SmallGroup(768,1087779)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 16, 192, 96
Order of s0s1s2 : 12
Order of s0s1s2s1 : 8
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 : {4,12}*384d, {4,24}*384e, {4,24}*384f
   4-fold quotients : {4,12}*192b, {4,6}*192b, {4,12}*192c
   8-fold quotients : {4,12}*96a, {4,12}*96b, {4,12}*96c, {4,6}*96
   16-fold quotients : {2,12}*48, {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   24-fold quotients : {4,4}*32
   32-fold quotients : {4,3}*24, {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 := (  1,199)(  2,200)(  3,197)(  4,198)(  5,196)(  6,195)(  7,194)(  8,193)
(  9,207)( 10,208)( 11,205)( 12,206)( 13,204)( 14,203)( 15,202)( 16,201)
( 17,215)( 18,216)( 19,213)( 20,214)( 21,212)( 22,211)( 23,210)( 24,209)
( 25,224)( 26,223)( 27,222)( 28,221)( 29,219)( 30,220)( 31,217)( 32,218)
( 33,232)( 34,231)( 35,230)( 36,229)( 37,227)( 38,228)( 39,225)( 40,226)
( 41,240)( 42,239)( 43,238)( 44,237)( 45,235)( 46,236)( 47,233)( 48,234)
( 49,248)( 50,247)( 51,246)( 52,245)( 53,243)( 54,244)( 55,241)( 56,242)
( 57,256)( 58,255)( 59,254)( 60,253)( 61,251)( 62,252)( 63,249)( 64,250)
( 65,264)( 66,263)( 67,262)( 68,261)( 69,259)( 70,260)( 71,257)( 72,258)
( 73,271)( 74,272)( 75,269)( 76,270)( 77,268)( 78,267)( 79,266)( 80,265)
( 81,279)( 82,280)( 83,277)( 84,278)( 85,276)( 86,275)( 87,274)( 88,273)
( 89,287)( 90,288)( 91,285)( 92,286)( 93,284)( 94,283)( 95,282)( 96,281)
( 97,343)( 98,344)( 99,341)(100,342)(101,340)(102,339)(103,338)(104,337)
(105,351)(106,352)(107,349)(108,350)(109,348)(110,347)(111,346)(112,345)
(113,359)(114,360)(115,357)(116,358)(117,356)(118,355)(119,354)(120,353)
(121,368)(122,367)(123,366)(124,365)(125,363)(126,364)(127,361)(128,362)
(129,376)(130,375)(131,374)(132,373)(133,371)(134,372)(135,369)(136,370)
(137,384)(138,383)(139,382)(140,381)(141,379)(142,380)(143,377)(144,378)
(145,295)(146,296)(147,293)(148,294)(149,292)(150,291)(151,290)(152,289)
(153,303)(154,304)(155,301)(156,302)(157,300)(158,299)(159,298)(160,297)
(161,311)(162,312)(163,309)(164,310)(165,308)(166,307)(167,306)(168,305)
(169,320)(170,319)(171,318)(172,317)(173,315)(174,316)(175,313)(176,314)
(177,328)(178,327)(179,326)(180,325)(181,323)(182,324)(183,321)(184,322)
(185,336)(186,335)(187,334)(188,333)(189,331)(190,332)(191,329)(192,330);;
s1 := (  1,121)(  2,122)(  3,124)(  4,123)(  5,127)(  6,128)(  7,125)(  8,126)
(  9,137)( 10,138)( 11,140)( 12,139)( 13,143)( 14,144)( 15,141)( 16,142)
( 17,129)( 18,130)( 19,132)( 20,131)( 21,135)( 22,136)( 23,133)( 24,134)
( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,103)( 30,104)( 31,101)( 32,102)
( 33,113)( 34,114)( 35,116)( 36,115)( 37,119)( 38,120)( 39,117)( 40,118)
( 41,105)( 42,106)( 43,108)( 44,107)( 45,111)( 46,112)( 47,109)( 48,110)
( 49,170)( 50,169)( 51,171)( 52,172)( 53,176)( 54,175)( 55,174)( 56,173)
( 57,186)( 58,185)( 59,187)( 60,188)( 61,192)( 62,191)( 63,190)( 64,189)
( 65,178)( 66,177)( 67,179)( 68,180)( 69,184)( 70,183)( 71,182)( 72,181)
( 73,146)( 74,145)( 75,147)( 76,148)( 77,152)( 78,151)( 79,150)( 80,149)
( 81,162)( 82,161)( 83,163)( 84,164)( 85,168)( 86,167)( 87,166)( 88,165)
( 89,154)( 90,153)( 91,155)( 92,156)( 93,160)( 94,159)( 95,158)( 96,157)
(193,313)(194,314)(195,316)(196,315)(197,319)(198,320)(199,317)(200,318)
(201,329)(202,330)(203,332)(204,331)(205,335)(206,336)(207,333)(208,334)
(209,321)(210,322)(211,324)(212,323)(213,327)(214,328)(215,325)(216,326)
(217,289)(218,290)(219,292)(220,291)(221,295)(222,296)(223,293)(224,294)
(225,305)(226,306)(227,308)(228,307)(229,311)(230,312)(231,309)(232,310)
(233,297)(234,298)(235,300)(236,299)(237,303)(238,304)(239,301)(240,302)
(241,362)(242,361)(243,363)(244,364)(245,368)(246,367)(247,366)(248,365)
(249,378)(250,377)(251,379)(252,380)(253,384)(254,383)(255,382)(256,381)
(257,370)(258,369)(259,371)(260,372)(261,376)(262,375)(263,374)(264,373)
(265,338)(266,337)(267,339)(268,340)(269,344)(270,343)(271,342)(272,341)
(273,354)(274,353)(275,355)(276,356)(277,360)(278,359)(279,358)(280,357)
(281,346)(282,345)(283,347)(284,348)(285,352)(286,351)(287,350)(288,349);;
s2 := (  1, 42)(  2, 41)(  3, 45)(  4, 46)(  5, 43)(  6, 44)(  7, 47)(  8, 48)
(  9, 34)( 10, 33)( 11, 37)( 12, 38)( 13, 35)( 14, 36)( 15, 39)( 16, 40)
( 17, 26)( 18, 25)( 19, 29)( 20, 30)( 21, 27)( 22, 28)( 23, 31)( 24, 32)
( 49, 89)( 50, 90)( 51, 94)( 52, 93)( 53, 92)( 54, 91)( 55, 96)( 56, 95)
( 57, 81)( 58, 82)( 59, 86)( 60, 85)( 61, 84)( 62, 83)( 63, 88)( 64, 87)
( 65, 73)( 66, 74)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 80)( 72, 79)
( 97,113)( 98,114)( 99,118)(100,117)(101,116)(102,115)(103,120)(104,119)
(107,110)(108,109)(111,112)(121,138)(122,137)(123,141)(124,142)(125,139)
(126,140)(127,143)(128,144)(129,130)(131,133)(132,134)(145,162)(146,161)
(147,165)(148,166)(149,163)(150,164)(151,167)(152,168)(153,154)(155,157)
(156,158)(169,185)(170,186)(171,190)(172,189)(173,188)(174,187)(175,192)
(176,191)(179,182)(180,181)(183,184)(193,234)(194,233)(195,237)(196,238)
(197,235)(198,236)(199,239)(200,240)(201,226)(202,225)(203,229)(204,230)
(205,227)(206,228)(207,231)(208,232)(209,218)(210,217)(211,221)(212,222)
(213,219)(214,220)(215,223)(216,224)(241,281)(242,282)(243,286)(244,285)
(245,284)(246,283)(247,288)(248,287)(249,273)(250,274)(251,278)(252,277)
(253,276)(254,275)(255,280)(256,279)(257,265)(258,266)(259,270)(260,269)
(261,268)(262,267)(263,272)(264,271)(289,305)(290,306)(291,310)(292,309)
(293,308)(294,307)(295,312)(296,311)(299,302)(300,301)(303,304)(313,330)
(314,329)(315,333)(316,334)(317,331)(318,332)(319,335)(320,336)(321,322)
(323,325)(324,326)(337,354)(338,353)(339,357)(340,358)(341,355)(342,356)
(343,359)(344,360)(345,346)(347,349)(348,350)(361,377)(362,378)(363,382)
(364,381)(365,380)(366,379)(367,384)(368,383)(371,374)(372,373)(375,376);;
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*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(384)!(  1,199)(  2,200)(  3,197)(  4,198)(  5,196)(  6,195)(  7,194)
(  8,193)(  9,207)( 10,208)( 11,205)( 12,206)( 13,204)( 14,203)( 15,202)
( 16,201)( 17,215)( 18,216)( 19,213)( 20,214)( 21,212)( 22,211)( 23,210)
( 24,209)( 25,224)( 26,223)( 27,222)( 28,221)( 29,219)( 30,220)( 31,217)
( 32,218)( 33,232)( 34,231)( 35,230)( 36,229)( 37,227)( 38,228)( 39,225)
( 40,226)( 41,240)( 42,239)( 43,238)( 44,237)( 45,235)( 46,236)( 47,233)
( 48,234)( 49,248)( 50,247)( 51,246)( 52,245)( 53,243)( 54,244)( 55,241)
( 56,242)( 57,256)( 58,255)( 59,254)( 60,253)( 61,251)( 62,252)( 63,249)
( 64,250)( 65,264)( 66,263)( 67,262)( 68,261)( 69,259)( 70,260)( 71,257)
( 72,258)( 73,271)( 74,272)( 75,269)( 76,270)( 77,268)( 78,267)( 79,266)
( 80,265)( 81,279)( 82,280)( 83,277)( 84,278)( 85,276)( 86,275)( 87,274)
( 88,273)( 89,287)( 90,288)( 91,285)( 92,286)( 93,284)( 94,283)( 95,282)
( 96,281)( 97,343)( 98,344)( 99,341)(100,342)(101,340)(102,339)(103,338)
(104,337)(105,351)(106,352)(107,349)(108,350)(109,348)(110,347)(111,346)
(112,345)(113,359)(114,360)(115,357)(116,358)(117,356)(118,355)(119,354)
(120,353)(121,368)(122,367)(123,366)(124,365)(125,363)(126,364)(127,361)
(128,362)(129,376)(130,375)(131,374)(132,373)(133,371)(134,372)(135,369)
(136,370)(137,384)(138,383)(139,382)(140,381)(141,379)(142,380)(143,377)
(144,378)(145,295)(146,296)(147,293)(148,294)(149,292)(150,291)(151,290)
(152,289)(153,303)(154,304)(155,301)(156,302)(157,300)(158,299)(159,298)
(160,297)(161,311)(162,312)(163,309)(164,310)(165,308)(166,307)(167,306)
(168,305)(169,320)(170,319)(171,318)(172,317)(173,315)(174,316)(175,313)
(176,314)(177,328)(178,327)(179,326)(180,325)(181,323)(182,324)(183,321)
(184,322)(185,336)(186,335)(187,334)(188,333)(189,331)(190,332)(191,329)
(192,330);
s1 := Sym(384)!(  1,121)(  2,122)(  3,124)(  4,123)(  5,127)(  6,128)(  7,125)
(  8,126)(  9,137)( 10,138)( 11,140)( 12,139)( 13,143)( 14,144)( 15,141)
( 16,142)( 17,129)( 18,130)( 19,132)( 20,131)( 21,135)( 22,136)( 23,133)
( 24,134)( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,103)( 30,104)( 31,101)
( 32,102)( 33,113)( 34,114)( 35,116)( 36,115)( 37,119)( 38,120)( 39,117)
( 40,118)( 41,105)( 42,106)( 43,108)( 44,107)( 45,111)( 46,112)( 47,109)
( 48,110)( 49,170)( 50,169)( 51,171)( 52,172)( 53,176)( 54,175)( 55,174)
( 56,173)( 57,186)( 58,185)( 59,187)( 60,188)( 61,192)( 62,191)( 63,190)
( 64,189)( 65,178)( 66,177)( 67,179)( 68,180)( 69,184)( 70,183)( 71,182)
( 72,181)( 73,146)( 74,145)( 75,147)( 76,148)( 77,152)( 78,151)( 79,150)
( 80,149)( 81,162)( 82,161)( 83,163)( 84,164)( 85,168)( 86,167)( 87,166)
( 88,165)( 89,154)( 90,153)( 91,155)( 92,156)( 93,160)( 94,159)( 95,158)
( 96,157)(193,313)(194,314)(195,316)(196,315)(197,319)(198,320)(199,317)
(200,318)(201,329)(202,330)(203,332)(204,331)(205,335)(206,336)(207,333)
(208,334)(209,321)(210,322)(211,324)(212,323)(213,327)(214,328)(215,325)
(216,326)(217,289)(218,290)(219,292)(220,291)(221,295)(222,296)(223,293)
(224,294)(225,305)(226,306)(227,308)(228,307)(229,311)(230,312)(231,309)
(232,310)(233,297)(234,298)(235,300)(236,299)(237,303)(238,304)(239,301)
(240,302)(241,362)(242,361)(243,363)(244,364)(245,368)(246,367)(247,366)
(248,365)(249,378)(250,377)(251,379)(252,380)(253,384)(254,383)(255,382)
(256,381)(257,370)(258,369)(259,371)(260,372)(261,376)(262,375)(263,374)
(264,373)(265,338)(266,337)(267,339)(268,340)(269,344)(270,343)(271,342)
(272,341)(273,354)(274,353)(275,355)(276,356)(277,360)(278,359)(279,358)
(280,357)(281,346)(282,345)(283,347)(284,348)(285,352)(286,351)(287,350)
(288,349);
s2 := Sym(384)!(  1, 42)(  2, 41)(  3, 45)(  4, 46)(  5, 43)(  6, 44)(  7, 47)
(  8, 48)(  9, 34)( 10, 33)( 11, 37)( 12, 38)( 13, 35)( 14, 36)( 15, 39)
( 16, 40)( 17, 26)( 18, 25)( 19, 29)( 20, 30)( 21, 27)( 22, 28)( 23, 31)
( 24, 32)( 49, 89)( 50, 90)( 51, 94)( 52, 93)( 53, 92)( 54, 91)( 55, 96)
( 56, 95)( 57, 81)( 58, 82)( 59, 86)( 60, 85)( 61, 84)( 62, 83)( 63, 88)
( 64, 87)( 65, 73)( 66, 74)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 80)
( 72, 79)( 97,113)( 98,114)( 99,118)(100,117)(101,116)(102,115)(103,120)
(104,119)(107,110)(108,109)(111,112)(121,138)(122,137)(123,141)(124,142)
(125,139)(126,140)(127,143)(128,144)(129,130)(131,133)(132,134)(145,162)
(146,161)(147,165)(148,166)(149,163)(150,164)(151,167)(152,168)(153,154)
(155,157)(156,158)(169,185)(170,186)(171,190)(172,189)(173,188)(174,187)
(175,192)(176,191)(179,182)(180,181)(183,184)(193,234)(194,233)(195,237)
(196,238)(197,235)(198,236)(199,239)(200,240)(201,226)(202,225)(203,229)
(204,230)(205,227)(206,228)(207,231)(208,232)(209,218)(210,217)(211,221)
(212,222)(213,219)(214,220)(215,223)(216,224)(241,281)(242,282)(243,286)
(244,285)(245,284)(246,283)(247,288)(248,287)(249,273)(250,274)(251,278)
(252,277)(253,276)(254,275)(255,280)(256,279)(257,265)(258,266)(259,270)
(260,269)(261,268)(262,267)(263,272)(264,271)(289,305)(290,306)(291,310)
(292,309)(293,308)(294,307)(295,312)(296,311)(299,302)(300,301)(303,304)
(313,330)(314,329)(315,333)(316,334)(317,331)(318,332)(319,335)(320,336)
(321,322)(323,325)(324,326)(337,354)(338,353)(339,357)(340,358)(341,355)
(342,356)(343,359)(344,360)(345,346)(347,349)(348,350)(361,377)(362,378)
(363,382)(364,381)(365,380)(366,379)(367,384)(368,383)(371,374)(372,373)
(375,376);
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*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >; 
 
References : None.
to this polytope