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Polytope of Type {24,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*768i
if this polytope has a name.
Group : SmallGroup(768,1086577)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 48, 192, 16
Order of s0s1s2 : 24
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
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 : {12,8}*384e, {24,4}*384c
   4-fold quotients : {24,4}*192c, {24,4}*192d, {12,4}*192b, {6,8}*192b
   8-fold quotients : {24,2}*96, {12,4}*96b, {12,4}*96c, {3,8}*96, {6,4}*96
   16-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   24-fold quotients : {8,2}*32
   32-fold quotients : {3,4}*24, {6,2}*24
   48-fold quotients : {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 := (  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)( 49, 73)( 50, 74)
( 51, 76)( 52, 75)( 53, 79)( 54, 80)( 55, 77)( 56, 78)( 57, 89)( 58, 90)
( 59, 92)( 60, 91)( 61, 95)( 62, 96)( 63, 93)( 64, 94)( 65, 81)( 66, 82)
( 67, 84)( 68, 83)( 69, 87)( 70, 88)( 71, 85)( 72, 86)( 97,145)( 98,146)
( 99,148)(100,147)(101,151)(102,152)(103,149)(104,150)(105,161)(106,162)
(107,164)(108,163)(109,167)(110,168)(111,165)(112,166)(113,153)(114,154)
(115,156)(116,155)(117,159)(118,160)(119,157)(120,158)(121,169)(122,170)
(123,172)(124,171)(125,175)(126,176)(127,173)(128,174)(129,185)(130,186)
(131,188)(132,187)(133,191)(134,192)(135,189)(136,190)(137,177)(138,178)
(139,180)(140,179)(141,183)(142,184)(143,181)(144,182)(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)(241,266)(242,265)(243,267)(244,268)
(245,272)(246,271)(247,270)(248,269)(249,282)(250,281)(251,283)(252,284)
(253,288)(254,287)(255,286)(256,285)(257,274)(258,273)(259,275)(260,276)
(261,280)(262,279)(263,278)(264,277)(289,338)(290,337)(291,339)(292,340)
(293,344)(294,343)(295,342)(296,341)(297,354)(298,353)(299,355)(300,356)
(301,360)(302,359)(303,358)(304,357)(305,346)(306,345)(307,347)(308,348)
(309,352)(310,351)(311,350)(312,349)(313,362)(314,361)(315,363)(316,364)
(317,368)(318,367)(319,366)(320,365)(321,378)(322,377)(323,379)(324,380)
(325,384)(326,383)(327,382)(328,381)(329,370)(330,369)(331,371)(332,372)
(333,376)(334,375)(335,374)(336,373);;
s1 := (  1,161)(  2,162)(  3,166)(  4,165)(  5,164)(  6,163)(  7,168)(  8,167)
(  9,153)( 10,154)( 11,158)( 12,157)( 13,156)( 14,155)( 15,160)( 16,159)
( 17,145)( 18,146)( 19,150)( 20,149)( 21,148)( 22,147)( 23,152)( 24,151)
( 25,185)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,192)( 32,191)
( 33,177)( 34,178)( 35,182)( 36,181)( 37,180)( 38,179)( 39,184)( 40,183)
( 41,169)( 42,170)( 43,174)( 44,173)( 45,172)( 46,171)( 47,176)( 48,175)
( 49,113)( 50,114)( 51,118)( 52,117)( 53,116)( 54,115)( 55,120)( 56,119)
( 57,105)( 58,106)( 59,110)( 60,109)( 61,108)( 62,107)( 63,112)( 64,111)
( 65, 97)( 66, 98)( 67,102)( 68,101)( 69,100)( 70, 99)( 71,104)( 72,103)
( 73,137)( 74,138)( 75,142)( 76,141)( 77,140)( 78,139)( 79,144)( 80,143)
( 81,129)( 82,130)( 83,134)( 84,133)( 85,132)( 86,131)( 87,136)( 88,135)
( 89,121)( 90,122)( 91,126)( 92,125)( 93,124)( 94,123)( 95,128)( 96,127)
(193,354)(194,353)(195,357)(196,358)(197,355)(198,356)(199,359)(200,360)
(201,346)(202,345)(203,349)(204,350)(205,347)(206,348)(207,351)(208,352)
(209,338)(210,337)(211,341)(212,342)(213,339)(214,340)(215,343)(216,344)
(217,378)(218,377)(219,381)(220,382)(221,379)(222,380)(223,383)(224,384)
(225,370)(226,369)(227,373)(228,374)(229,371)(230,372)(231,375)(232,376)
(233,362)(234,361)(235,365)(236,366)(237,363)(238,364)(239,367)(240,368)
(241,306)(242,305)(243,309)(244,310)(245,307)(246,308)(247,311)(248,312)
(249,298)(250,297)(251,301)(252,302)(253,299)(254,300)(255,303)(256,304)
(257,290)(258,289)(259,293)(260,294)(261,291)(262,292)(263,295)(264,296)
(265,330)(266,329)(267,333)(268,334)(269,331)(270,332)(271,335)(272,336)
(273,322)(274,321)(275,325)(276,326)(277,323)(278,324)(279,327)(280,328)
(281,314)(282,313)(283,317)(284,318)(285,315)(286,316)(287,319)(288,320);;
s2 := (  1,196)(  2,195)(  3,193)(  4,194)(  5,200)(  6,199)(  7,197)(  8,198)
(  9,204)( 10,203)( 11,201)( 12,202)( 13,208)( 14,207)( 15,205)( 16,206)
( 17,212)( 18,211)( 19,209)( 20,210)( 21,216)( 22,215)( 23,213)( 24,214)
( 25,220)( 26,219)( 27,217)( 28,218)( 29,224)( 30,223)( 31,221)( 32,222)
( 33,228)( 34,227)( 35,225)( 36,226)( 37,232)( 38,231)( 39,229)( 40,230)
( 41,236)( 42,235)( 43,233)( 44,234)( 45,240)( 46,239)( 47,237)( 48,238)
( 49,244)( 50,243)( 51,241)( 52,242)( 53,248)( 54,247)( 55,245)( 56,246)
( 57,252)( 58,251)( 59,249)( 60,250)( 61,256)( 62,255)( 63,253)( 64,254)
( 65,260)( 66,259)( 67,257)( 68,258)( 69,264)( 70,263)( 71,261)( 72,262)
( 73,268)( 74,267)( 75,265)( 76,266)( 77,272)( 78,271)( 79,269)( 80,270)
( 81,276)( 82,275)( 83,273)( 84,274)( 85,280)( 86,279)( 87,277)( 88,278)
( 89,284)( 90,283)( 91,281)( 92,282)( 93,288)( 94,287)( 95,285)( 96,286)
( 97,292)( 98,291)( 99,289)(100,290)(101,296)(102,295)(103,293)(104,294)
(105,300)(106,299)(107,297)(108,298)(109,304)(110,303)(111,301)(112,302)
(113,308)(114,307)(115,305)(116,306)(117,312)(118,311)(119,309)(120,310)
(121,316)(122,315)(123,313)(124,314)(125,320)(126,319)(127,317)(128,318)
(129,324)(130,323)(131,321)(132,322)(133,328)(134,327)(135,325)(136,326)
(137,332)(138,331)(139,329)(140,330)(141,336)(142,335)(143,333)(144,334)
(145,340)(146,339)(147,337)(148,338)(149,344)(150,343)(151,341)(152,342)
(153,348)(154,347)(155,345)(156,346)(157,352)(158,351)(159,349)(160,350)
(161,356)(162,355)(163,353)(164,354)(165,360)(166,359)(167,357)(168,358)
(169,364)(170,363)(171,361)(172,362)(173,368)(174,367)(175,365)(176,366)
(177,372)(178,371)(179,369)(180,370)(181,376)(182,375)(183,373)(184,374)
(185,380)(186,379)(187,377)(188,378)(189,384)(190,383)(191,381)(192,382);;
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*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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*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)( 49, 73)
( 50, 74)( 51, 76)( 52, 75)( 53, 79)( 54, 80)( 55, 77)( 56, 78)( 57, 89)
( 58, 90)( 59, 92)( 60, 91)( 61, 95)( 62, 96)( 63, 93)( 64, 94)( 65, 81)
( 66, 82)( 67, 84)( 68, 83)( 69, 87)( 70, 88)( 71, 85)( 72, 86)( 97,145)
( 98,146)( 99,148)(100,147)(101,151)(102,152)(103,149)(104,150)(105,161)
(106,162)(107,164)(108,163)(109,167)(110,168)(111,165)(112,166)(113,153)
(114,154)(115,156)(116,155)(117,159)(118,160)(119,157)(120,158)(121,169)
(122,170)(123,172)(124,171)(125,175)(126,176)(127,173)(128,174)(129,185)
(130,186)(131,188)(132,187)(133,191)(134,192)(135,189)(136,190)(137,177)
(138,178)(139,180)(140,179)(141,183)(142,184)(143,181)(144,182)(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)(241,266)(242,265)(243,267)
(244,268)(245,272)(246,271)(247,270)(248,269)(249,282)(250,281)(251,283)
(252,284)(253,288)(254,287)(255,286)(256,285)(257,274)(258,273)(259,275)
(260,276)(261,280)(262,279)(263,278)(264,277)(289,338)(290,337)(291,339)
(292,340)(293,344)(294,343)(295,342)(296,341)(297,354)(298,353)(299,355)
(300,356)(301,360)(302,359)(303,358)(304,357)(305,346)(306,345)(307,347)
(308,348)(309,352)(310,351)(311,350)(312,349)(313,362)(314,361)(315,363)
(316,364)(317,368)(318,367)(319,366)(320,365)(321,378)(322,377)(323,379)
(324,380)(325,384)(326,383)(327,382)(328,381)(329,370)(330,369)(331,371)
(332,372)(333,376)(334,375)(335,374)(336,373);
s1 := Sym(384)!(  1,161)(  2,162)(  3,166)(  4,165)(  5,164)(  6,163)(  7,168)
(  8,167)(  9,153)( 10,154)( 11,158)( 12,157)( 13,156)( 14,155)( 15,160)
( 16,159)( 17,145)( 18,146)( 19,150)( 20,149)( 21,148)( 22,147)( 23,152)
( 24,151)( 25,185)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,192)
( 32,191)( 33,177)( 34,178)( 35,182)( 36,181)( 37,180)( 38,179)( 39,184)
( 40,183)( 41,169)( 42,170)( 43,174)( 44,173)( 45,172)( 46,171)( 47,176)
( 48,175)( 49,113)( 50,114)( 51,118)( 52,117)( 53,116)( 54,115)( 55,120)
( 56,119)( 57,105)( 58,106)( 59,110)( 60,109)( 61,108)( 62,107)( 63,112)
( 64,111)( 65, 97)( 66, 98)( 67,102)( 68,101)( 69,100)( 70, 99)( 71,104)
( 72,103)( 73,137)( 74,138)( 75,142)( 76,141)( 77,140)( 78,139)( 79,144)
( 80,143)( 81,129)( 82,130)( 83,134)( 84,133)( 85,132)( 86,131)( 87,136)
( 88,135)( 89,121)( 90,122)( 91,126)( 92,125)( 93,124)( 94,123)( 95,128)
( 96,127)(193,354)(194,353)(195,357)(196,358)(197,355)(198,356)(199,359)
(200,360)(201,346)(202,345)(203,349)(204,350)(205,347)(206,348)(207,351)
(208,352)(209,338)(210,337)(211,341)(212,342)(213,339)(214,340)(215,343)
(216,344)(217,378)(218,377)(219,381)(220,382)(221,379)(222,380)(223,383)
(224,384)(225,370)(226,369)(227,373)(228,374)(229,371)(230,372)(231,375)
(232,376)(233,362)(234,361)(235,365)(236,366)(237,363)(238,364)(239,367)
(240,368)(241,306)(242,305)(243,309)(244,310)(245,307)(246,308)(247,311)
(248,312)(249,298)(250,297)(251,301)(252,302)(253,299)(254,300)(255,303)
(256,304)(257,290)(258,289)(259,293)(260,294)(261,291)(262,292)(263,295)
(264,296)(265,330)(266,329)(267,333)(268,334)(269,331)(270,332)(271,335)
(272,336)(273,322)(274,321)(275,325)(276,326)(277,323)(278,324)(279,327)
(280,328)(281,314)(282,313)(283,317)(284,318)(285,315)(286,316)(287,319)
(288,320);
s2 := Sym(384)!(  1,196)(  2,195)(  3,193)(  4,194)(  5,200)(  6,199)(  7,197)
(  8,198)(  9,204)( 10,203)( 11,201)( 12,202)( 13,208)( 14,207)( 15,205)
( 16,206)( 17,212)( 18,211)( 19,209)( 20,210)( 21,216)( 22,215)( 23,213)
( 24,214)( 25,220)( 26,219)( 27,217)( 28,218)( 29,224)( 30,223)( 31,221)
( 32,222)( 33,228)( 34,227)( 35,225)( 36,226)( 37,232)( 38,231)( 39,229)
( 40,230)( 41,236)( 42,235)( 43,233)( 44,234)( 45,240)( 46,239)( 47,237)
( 48,238)( 49,244)( 50,243)( 51,241)( 52,242)( 53,248)( 54,247)( 55,245)
( 56,246)( 57,252)( 58,251)( 59,249)( 60,250)( 61,256)( 62,255)( 63,253)
( 64,254)( 65,260)( 66,259)( 67,257)( 68,258)( 69,264)( 70,263)( 71,261)
( 72,262)( 73,268)( 74,267)( 75,265)( 76,266)( 77,272)( 78,271)( 79,269)
( 80,270)( 81,276)( 82,275)( 83,273)( 84,274)( 85,280)( 86,279)( 87,277)
( 88,278)( 89,284)( 90,283)( 91,281)( 92,282)( 93,288)( 94,287)( 95,285)
( 96,286)( 97,292)( 98,291)( 99,289)(100,290)(101,296)(102,295)(103,293)
(104,294)(105,300)(106,299)(107,297)(108,298)(109,304)(110,303)(111,301)
(112,302)(113,308)(114,307)(115,305)(116,306)(117,312)(118,311)(119,309)
(120,310)(121,316)(122,315)(123,313)(124,314)(125,320)(126,319)(127,317)
(128,318)(129,324)(130,323)(131,321)(132,322)(133,328)(134,327)(135,325)
(136,326)(137,332)(138,331)(139,329)(140,330)(141,336)(142,335)(143,333)
(144,334)(145,340)(146,339)(147,337)(148,338)(149,344)(150,343)(151,341)
(152,342)(153,348)(154,347)(155,345)(156,346)(157,352)(158,351)(159,349)
(160,350)(161,356)(162,355)(163,353)(164,354)(165,360)(166,359)(167,357)
(168,358)(169,364)(170,363)(171,361)(172,362)(173,368)(174,367)(175,365)
(176,366)(177,372)(178,371)(179,369)(180,370)(181,376)(182,375)(183,373)
(184,374)(185,380)(186,379)(187,377)(188,378)(189,384)(190,383)(191,381)
(192,382);
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*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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*s0*s1 >; 
 
References : None.
to this polytope