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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}*768g
if this polytope has a name.
Group : SmallGroup(768,90328)
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
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 : {24,4}*384b
   3-fold quotients : {8,8}*256h
   4-fold quotients : {12,4}*192a
   6-fold quotients : {8,4}*128b
   8-fold quotients : {12,4}*96a
   12-fold quotients : {4,4}*64
   16-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {4,4}*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 := (  1,289)(  2,291)(  3,290)(  4,292)(  5,294)(  6,293)(  7,295)(  8,297)
(  9,296)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)( 16,301)
( 17,303)( 18,302)( 19,310)( 20,312)( 21,311)( 22,307)( 23,309)( 24,308)
( 25,331)( 26,333)( 27,332)( 28,334)( 29,336)( 30,335)( 31,325)( 32,327)
( 33,326)( 34,328)( 35,330)( 36,329)( 37,319)( 38,321)( 39,320)( 40,322)
( 41,324)( 42,323)( 43,313)( 44,315)( 45,314)( 46,316)( 47,318)( 48,317)
( 49,352)( 50,354)( 51,353)( 52,349)( 53,351)( 54,350)( 55,358)( 56,360)
( 57,359)( 58,355)( 59,357)( 60,356)( 61,340)( 62,342)( 63,341)( 64,337)
( 65,339)( 66,338)( 67,346)( 68,348)( 69,347)( 70,343)( 71,345)( 72,344)
( 73,370)( 74,372)( 75,371)( 76,367)( 77,369)( 78,368)( 79,364)( 80,366)
( 81,365)( 82,361)( 83,363)( 84,362)( 85,379)( 86,381)( 87,380)( 88,382)
( 89,384)( 90,383)( 91,373)( 92,375)( 93,374)( 94,376)( 95,378)( 96,377)
( 97,193)( 98,195)( 99,194)(100,196)(101,198)(102,197)(103,199)(104,201)
(105,200)(106,202)(107,204)(108,203)(109,208)(110,210)(111,209)(112,205)
(113,207)(114,206)(115,214)(116,216)(117,215)(118,211)(119,213)(120,212)
(121,235)(122,237)(123,236)(124,238)(125,240)(126,239)(127,229)(128,231)
(129,230)(130,232)(131,234)(132,233)(133,223)(134,225)(135,224)(136,226)
(137,228)(138,227)(139,217)(140,219)(141,218)(142,220)(143,222)(144,221)
(145,256)(146,258)(147,257)(148,253)(149,255)(150,254)(151,262)(152,264)
(153,263)(154,259)(155,261)(156,260)(157,244)(158,246)(159,245)(160,241)
(161,243)(162,242)(163,250)(164,252)(165,251)(166,247)(167,249)(168,248)
(169,274)(170,276)(171,275)(172,271)(173,273)(174,272)(175,268)(176,270)
(177,269)(178,265)(179,267)(180,266)(181,283)(182,285)(183,284)(184,286)
(185,288)(186,287)(187,277)(188,279)(189,278)(190,280)(191,282)(192,281);;
s1 := (  1,  3)(  4,  6)(  7,  9)( 10, 12)( 13, 21)( 14, 20)( 15, 19)( 16, 24)
( 17, 23)( 18, 22)( 25, 30)( 26, 29)( 27, 28)( 31, 36)( 32, 35)( 33, 34)
( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)( 42, 43)( 49, 54)( 50, 53)
( 51, 52)( 55, 60)( 56, 59)( 57, 58)( 61, 72)( 62, 71)( 63, 70)( 64, 69)
( 65, 68)( 66, 67)( 73, 75)( 76, 78)( 79, 81)( 82, 84)( 85, 93)( 86, 92)
( 87, 91)( 88, 96)( 89, 95)( 90, 94)( 97,123)( 98,122)( 99,121)(100,126)
(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)(107,131)(108,130)
(109,141)(110,140)(111,139)(112,144)(113,143)(114,142)(115,135)(116,134)
(117,133)(118,138)(119,137)(120,136)(145,177)(146,176)(147,175)(148,180)
(149,179)(150,178)(151,171)(152,170)(153,169)(154,174)(155,173)(156,172)
(157,183)(158,182)(159,181)(160,186)(161,185)(162,184)(163,189)(164,188)
(165,187)(166,192)(167,191)(168,190)(193,243)(194,242)(195,241)(196,246)
(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)(203,251)(204,250)
(205,261)(206,260)(207,259)(208,264)(209,263)(210,262)(211,255)(212,254)
(213,253)(214,258)(215,257)(216,256)(217,270)(218,269)(219,268)(220,267)
(221,266)(222,265)(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)
(229,288)(230,287)(231,286)(232,285)(233,284)(234,283)(235,282)(236,281)
(237,280)(238,279)(239,278)(240,277)(289,378)(290,377)(291,376)(292,375)
(293,374)(294,373)(295,384)(296,383)(297,382)(298,381)(299,380)(300,379)
(301,369)(302,368)(303,367)(304,372)(305,371)(306,370)(307,363)(308,362)
(309,361)(310,366)(311,365)(312,364)(313,351)(314,350)(315,349)(316,354)
(317,353)(318,352)(319,357)(320,356)(321,355)(322,360)(323,359)(324,358)
(325,348)(326,347)(327,346)(328,345)(329,344)(330,343)(331,342)(332,341)
(333,340)(334,339)(335,338)(336,337);;
s2 := (  1,193)(  2,194)(  3,195)(  4,196)(  5,197)(  6,198)(  7,202)(  8,203)
(  9,204)( 10,199)( 11,200)( 12,201)( 13,205)( 14,206)( 15,207)( 16,208)
( 17,209)( 18,210)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)( 24,213)
( 25,238)( 26,239)( 27,240)( 28,235)( 29,236)( 30,237)( 31,229)( 32,230)
( 33,231)( 34,232)( 35,233)( 36,234)( 37,223)( 38,224)( 39,225)( 40,226)
( 41,227)( 42,228)( 43,220)( 44,221)( 45,222)( 46,217)( 47,218)( 48,219)
( 49,244)( 50,245)( 51,246)( 52,241)( 53,242)( 54,243)( 55,247)( 56,248)
( 57,249)( 58,250)( 59,251)( 60,252)( 61,256)( 62,257)( 63,258)( 64,253)
( 65,254)( 66,255)( 67,259)( 68,260)( 69,261)( 70,262)( 71,263)( 72,264)
( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,280)( 80,281)
( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)( 88,271)
( 89,272)( 90,273)( 91,265)( 92,266)( 93,267)( 94,268)( 95,269)( 96,270)
( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)(104,299)
(105,300)(106,295)(107,296)(108,297)(109,301)(110,302)(111,303)(112,304)
(113,305)(114,306)(115,310)(116,311)(117,312)(118,307)(119,308)(120,309)
(121,334)(122,335)(123,336)(124,331)(125,332)(126,333)(127,325)(128,326)
(129,327)(130,328)(131,329)(132,330)(133,319)(134,320)(135,321)(136,322)
(137,323)(138,324)(139,316)(140,317)(141,318)(142,313)(143,314)(144,315)
(145,340)(146,341)(147,342)(148,337)(149,338)(150,339)(151,343)(152,344)
(153,345)(154,346)(155,347)(156,348)(157,352)(158,353)(159,354)(160,349)
(161,350)(162,351)(163,355)(164,356)(165,357)(166,358)(167,359)(168,360)
(169,379)(170,380)(171,381)(172,382)(173,383)(174,384)(175,376)(176,377)
(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)(184,367)
(185,368)(186,369)(187,361)(188,362)(189,363)(190,364)(191,365)(192,366);;
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*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(384)!(  1,289)(  2,291)(  3,290)(  4,292)(  5,294)(  6,293)(  7,295)
(  8,297)(  9,296)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)
( 16,301)( 17,303)( 18,302)( 19,310)( 20,312)( 21,311)( 22,307)( 23,309)
( 24,308)( 25,331)( 26,333)( 27,332)( 28,334)( 29,336)( 30,335)( 31,325)
( 32,327)( 33,326)( 34,328)( 35,330)( 36,329)( 37,319)( 38,321)( 39,320)
( 40,322)( 41,324)( 42,323)( 43,313)( 44,315)( 45,314)( 46,316)( 47,318)
( 48,317)( 49,352)( 50,354)( 51,353)( 52,349)( 53,351)( 54,350)( 55,358)
( 56,360)( 57,359)( 58,355)( 59,357)( 60,356)( 61,340)( 62,342)( 63,341)
( 64,337)( 65,339)( 66,338)( 67,346)( 68,348)( 69,347)( 70,343)( 71,345)
( 72,344)( 73,370)( 74,372)( 75,371)( 76,367)( 77,369)( 78,368)( 79,364)
( 80,366)( 81,365)( 82,361)( 83,363)( 84,362)( 85,379)( 86,381)( 87,380)
( 88,382)( 89,384)( 90,383)( 91,373)( 92,375)( 93,374)( 94,376)( 95,378)
( 96,377)( 97,193)( 98,195)( 99,194)(100,196)(101,198)(102,197)(103,199)
(104,201)(105,200)(106,202)(107,204)(108,203)(109,208)(110,210)(111,209)
(112,205)(113,207)(114,206)(115,214)(116,216)(117,215)(118,211)(119,213)
(120,212)(121,235)(122,237)(123,236)(124,238)(125,240)(126,239)(127,229)
(128,231)(129,230)(130,232)(131,234)(132,233)(133,223)(134,225)(135,224)
(136,226)(137,228)(138,227)(139,217)(140,219)(141,218)(142,220)(143,222)
(144,221)(145,256)(146,258)(147,257)(148,253)(149,255)(150,254)(151,262)
(152,264)(153,263)(154,259)(155,261)(156,260)(157,244)(158,246)(159,245)
(160,241)(161,243)(162,242)(163,250)(164,252)(165,251)(166,247)(167,249)
(168,248)(169,274)(170,276)(171,275)(172,271)(173,273)(174,272)(175,268)
(176,270)(177,269)(178,265)(179,267)(180,266)(181,283)(182,285)(183,284)
(184,286)(185,288)(186,287)(187,277)(188,279)(189,278)(190,280)(191,282)
(192,281);
s1 := Sym(384)!(  1,  3)(  4,  6)(  7,  9)( 10, 12)( 13, 21)( 14, 20)( 15, 19)
( 16, 24)( 17, 23)( 18, 22)( 25, 30)( 26, 29)( 27, 28)( 31, 36)( 32, 35)
( 33, 34)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)( 42, 43)( 49, 54)
( 50, 53)( 51, 52)( 55, 60)( 56, 59)( 57, 58)( 61, 72)( 62, 71)( 63, 70)
( 64, 69)( 65, 68)( 66, 67)( 73, 75)( 76, 78)( 79, 81)( 82, 84)( 85, 93)
( 86, 92)( 87, 91)( 88, 96)( 89, 95)( 90, 94)( 97,123)( 98,122)( 99,121)
(100,126)(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)(107,131)
(108,130)(109,141)(110,140)(111,139)(112,144)(113,143)(114,142)(115,135)
(116,134)(117,133)(118,138)(119,137)(120,136)(145,177)(146,176)(147,175)
(148,180)(149,179)(150,178)(151,171)(152,170)(153,169)(154,174)(155,173)
(156,172)(157,183)(158,182)(159,181)(160,186)(161,185)(162,184)(163,189)
(164,188)(165,187)(166,192)(167,191)(168,190)(193,243)(194,242)(195,241)
(196,246)(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)(203,251)
(204,250)(205,261)(206,260)(207,259)(208,264)(209,263)(210,262)(211,255)
(212,254)(213,253)(214,258)(215,257)(216,256)(217,270)(218,269)(219,268)
(220,267)(221,266)(222,265)(223,276)(224,275)(225,274)(226,273)(227,272)
(228,271)(229,288)(230,287)(231,286)(232,285)(233,284)(234,283)(235,282)
(236,281)(237,280)(238,279)(239,278)(240,277)(289,378)(290,377)(291,376)
(292,375)(293,374)(294,373)(295,384)(296,383)(297,382)(298,381)(299,380)
(300,379)(301,369)(302,368)(303,367)(304,372)(305,371)(306,370)(307,363)
(308,362)(309,361)(310,366)(311,365)(312,364)(313,351)(314,350)(315,349)
(316,354)(317,353)(318,352)(319,357)(320,356)(321,355)(322,360)(323,359)
(324,358)(325,348)(326,347)(327,346)(328,345)(329,344)(330,343)(331,342)
(332,341)(333,340)(334,339)(335,338)(336,337);
s2 := Sym(384)!(  1,193)(  2,194)(  3,195)(  4,196)(  5,197)(  6,198)(  7,202)
(  8,203)(  9,204)( 10,199)( 11,200)( 12,201)( 13,205)( 14,206)( 15,207)
( 16,208)( 17,209)( 18,210)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)
( 24,213)( 25,238)( 26,239)( 27,240)( 28,235)( 29,236)( 30,237)( 31,229)
( 32,230)( 33,231)( 34,232)( 35,233)( 36,234)( 37,223)( 38,224)( 39,225)
( 40,226)( 41,227)( 42,228)( 43,220)( 44,221)( 45,222)( 46,217)( 47,218)
( 48,219)( 49,244)( 50,245)( 51,246)( 52,241)( 53,242)( 54,243)( 55,247)
( 56,248)( 57,249)( 58,250)( 59,251)( 60,252)( 61,256)( 62,257)( 63,258)
( 64,253)( 65,254)( 66,255)( 67,259)( 68,260)( 69,261)( 70,262)( 71,263)
( 72,264)( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,280)
( 80,281)( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)
( 88,271)( 89,272)( 90,273)( 91,265)( 92,266)( 93,267)( 94,268)( 95,269)
( 96,270)( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)
(104,299)(105,300)(106,295)(107,296)(108,297)(109,301)(110,302)(111,303)
(112,304)(113,305)(114,306)(115,310)(116,311)(117,312)(118,307)(119,308)
(120,309)(121,334)(122,335)(123,336)(124,331)(125,332)(126,333)(127,325)
(128,326)(129,327)(130,328)(131,329)(132,330)(133,319)(134,320)(135,321)
(136,322)(137,323)(138,324)(139,316)(140,317)(141,318)(142,313)(143,314)
(144,315)(145,340)(146,341)(147,342)(148,337)(149,338)(150,339)(151,343)
(152,344)(153,345)(154,346)(155,347)(156,348)(157,352)(158,353)(159,354)
(160,349)(161,350)(162,351)(163,355)(164,356)(165,357)(166,358)(167,359)
(168,360)(169,379)(170,380)(171,381)(172,382)(173,383)(174,384)(175,376)
(176,377)(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)
(184,367)(185,368)(186,369)(187,361)(188,362)(189,363)(190,364)(191,365)
(192,366);
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*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0 >; 
 
References : None.
to this polytope