Polytope of Type {8,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,24}*768i
if this polytope has a name.
Group : SmallGroup(768,1086577)
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}*384e, {4,24}*384c
4-fold quotients : {4,24}*192c, {4,24}*192d, {4,12}*192b, {8,6}*192b
8-fold quotients : {2,24}*96, {4,12}*96b, {4,12}*96c, {8,3}*96, {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)
( 97,295)( 98,296)( 99,293)(100,294)(101,292)(102,291)(103,290)(104,289)
(105,303)(106,304)(107,301)(108,302)(109,300)(110,299)(111,298)(112,297)
(113,311)(114,312)(115,309)(116,310)(117,308)(118,307)(119,306)(120,305)
(121,319)(122,320)(123,317)(124,318)(125,316)(126,315)(127,314)(128,313)
(129,327)(130,328)(131,325)(132,326)(133,324)(134,323)(135,322)(136,321)
(137,335)(138,336)(139,333)(140,334)(141,332)(142,331)(143,330)(144,329)
(145,343)(146,344)(147,341)(148,342)(149,340)(150,339)(151,338)(152,337)
(153,351)(154,352)(155,349)(156,350)(157,348)(158,347)(159,346)(160,345)
(161,359)(162,360)(163,357)(164,358)(165,356)(166,355)(167,354)(168,353)
(169,367)(170,368)(171,365)(172,366)(173,364)(174,363)(175,362)(176,361)
(177,375)(178,376)(179,373)(180,374)(181,372)(182,371)(183,370)(184,369)
(185,383)(186,384)(187,381)(188,382)(189,380)(190,379)(191,378)(192,377);;
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)(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);;
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)
(193,354)(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);;
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*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*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)( 97,295)( 98,296)( 99,293)(100,294)(101,292)(102,291)(103,290)
(104,289)(105,303)(106,304)(107,301)(108,302)(109,300)(110,299)(111,298)
(112,297)(113,311)(114,312)(115,309)(116,310)(117,308)(118,307)(119,306)
(120,305)(121,319)(122,320)(123,317)(124,318)(125,316)(126,315)(127,314)
(128,313)(129,327)(130,328)(131,325)(132,326)(133,324)(134,323)(135,322)
(136,321)(137,335)(138,336)(139,333)(140,334)(141,332)(142,331)(143,330)
(144,329)(145,343)(146,344)(147,341)(148,342)(149,340)(150,339)(151,338)
(152,337)(153,351)(154,352)(155,349)(156,350)(157,348)(158,347)(159,346)
(160,345)(161,359)(162,360)(163,357)(164,358)(165,356)(166,355)(167,354)
(168,353)(169,367)(170,368)(171,365)(172,366)(173,364)(174,363)(175,362)
(176,361)(177,375)(178,376)(179,373)(180,374)(181,372)(182,371)(183,370)
(184,369)(185,383)(186,384)(187,381)(188,382)(189,380)(190,379)(191,378)
(192,377);
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)(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);
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)(193,354)(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);
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*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*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