Polytope of Type {24,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*768k
if this polytope has a name.
Group : SmallGroup(768,1086615)
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}*384f, {24,4}*384c
   4-fold quotients : {24,4}*192c, {24,4}*192d, {12,4}*192b, {6,8}*192c
   8-fold quotients : {24,2}*96, {12,4}*96b, {12,4}*96c, {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 := (  1,145)(  2,146)(  3,148)(  4,147)(  5,151)(  6,152)(  7,149)(  8,150)
(  9,161)( 10,162)( 11,164)( 12,163)( 13,167)( 14,168)( 15,165)( 16,166)
( 17,153)( 18,154)( 19,156)( 20,155)( 21,159)( 22,160)( 23,157)( 24,158)
( 25,169)( 26,170)( 27,172)( 28,171)( 29,175)( 30,176)( 31,173)( 32,174)
( 33,185)( 34,186)( 35,188)( 36,187)( 37,191)( 38,192)( 39,189)( 40,190)
( 41,177)( 42,178)( 43,180)( 44,179)( 45,183)( 46,184)( 47,181)( 48,182)
( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,103)( 54,104)( 55,101)( 56,102)
( 57,113)( 58,114)( 59,116)( 60,115)( 61,119)( 62,120)( 63,117)( 64,118)
( 65,105)( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)
( 73,121)( 74,122)( 75,124)( 76,123)( 77,127)( 78,128)( 79,125)( 80,126)
( 81,137)( 82,138)( 83,140)( 84,139)( 85,143)( 86,144)( 87,141)( 88,142)
( 89,129)( 90,130)( 91,132)( 92,131)( 93,135)( 94,136)( 95,133)( 96,134)
(193,337)(194,338)(195,340)(196,339)(197,343)(198,344)(199,341)(200,342)
(201,353)(202,354)(203,356)(204,355)(205,359)(206,360)(207,357)(208,358)
(209,345)(210,346)(211,348)(212,347)(213,351)(214,352)(215,349)(216,350)
(217,361)(218,362)(219,364)(220,363)(221,367)(222,368)(223,365)(224,366)
(225,377)(226,378)(227,380)(228,379)(229,383)(230,384)(231,381)(232,382)
(233,369)(234,370)(235,372)(236,371)(237,375)(238,376)(239,373)(240,374)
(241,289)(242,290)(243,292)(244,291)(245,295)(246,296)(247,293)(248,294)
(249,305)(250,306)(251,308)(252,307)(253,311)(254,312)(255,309)(256,310)
(257,297)(258,298)(259,300)(260,299)(261,303)(262,304)(263,301)(264,302)
(265,313)(266,314)(267,316)(268,315)(269,319)(270,320)(271,317)(272,318)
(273,329)(274,330)(275,332)(276,331)(277,335)(278,336)(279,333)(280,334)
(281,321)(282,322)(283,324)(284,323)(285,327)(286,328)(287,325)(288,326);;
s1 := (  1, 17)(  2, 18)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 24)(  8, 23)
( 11, 14)( 12, 13)( 15, 16)( 25, 41)( 26, 42)( 27, 46)( 28, 45)( 29, 44)
( 30, 43)( 31, 48)( 32, 47)( 35, 38)( 36, 37)( 39, 40)( 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)( 97,161)( 98,162)
( 99,166)(100,165)(101,164)(102,163)(103,168)(104,167)(105,153)(106,154)
(107,158)(108,157)(109,156)(110,155)(111,160)(112,159)(113,145)(114,146)
(115,150)(116,149)(117,148)(118,147)(119,152)(120,151)(121,185)(122,186)
(123,190)(124,189)(125,188)(126,187)(127,192)(128,191)(129,177)(130,178)
(131,182)(132,181)(133,180)(134,179)(135,184)(136,183)(137,169)(138,170)
(139,174)(140,173)(141,172)(142,171)(143,176)(144,175)(193,209)(194,210)
(195,214)(196,213)(197,212)(198,211)(199,216)(200,215)(203,206)(204,205)
(207,208)(217,233)(218,234)(219,238)(220,237)(221,236)(222,235)(223,240)
(224,239)(227,230)(228,229)(231,232)(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)(289,353)(290,354)(291,358)(292,357)
(293,356)(294,355)(295,360)(296,359)(297,345)(298,346)(299,350)(300,349)
(301,348)(302,347)(303,352)(304,351)(305,337)(306,338)(307,342)(308,341)
(309,340)(310,339)(311,344)(312,343)(313,377)(314,378)(315,382)(316,381)
(317,380)(318,379)(319,384)(320,383)(321,369)(322,370)(323,374)(324,373)
(325,372)(326,371)(327,376)(328,375)(329,361)(330,362)(331,366)(332,365)
(333,364)(334,363)(335,368)(336,367);;
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)
( 97,291)( 98,292)( 99,290)(100,289)(101,295)(102,296)(103,294)(104,293)
(105,299)(106,300)(107,298)(108,297)(109,303)(110,304)(111,302)(112,301)
(113,307)(114,308)(115,306)(116,305)(117,311)(118,312)(119,310)(120,309)
(121,315)(122,316)(123,314)(124,313)(125,319)(126,320)(127,318)(128,317)
(129,323)(130,324)(131,322)(132,321)(133,327)(134,328)(135,326)(136,325)
(137,331)(138,332)(139,330)(140,329)(141,335)(142,336)(143,334)(144,333)
(145,339)(146,340)(147,338)(148,337)(149,343)(150,344)(151,342)(152,341)
(153,347)(154,348)(155,346)(156,345)(157,351)(158,352)(159,350)(160,349)
(161,355)(162,356)(163,354)(164,353)(165,359)(166,360)(167,358)(168,357)
(169,363)(170,364)(171,362)(172,361)(173,367)(174,368)(175,366)(176,365)
(177,371)(178,372)(179,370)(180,369)(181,375)(182,376)(183,374)(184,373)
(185,379)(186,380)(187,378)(188,377)(189,383)(190,384)(191,382)(192,381);;
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*s2*s0*s1*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*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope