Polytope of Type {8,24}

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

References : None.
to this polytope