Polytope of Type {8,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,24}*768c
if this polytope has a name.
Group : SmallGroup(768,81632)
Rank : 3
Schlafli Type : {8,24}
Number of vertices, edges, etc : 16, 192, 48
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
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}*384a, {4,24}*384b
3-fold quotients : {8,8}*256d
4-fold quotients : {4,12}*192a, {8,12}*192a, {8,12}*192b
6-fold quotients : {8,4}*128a, {4,8}*128b
8-fold quotients : {4,12}*96a, {8,6}*96
12-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
16-fold quotients : {2,12}*48, {4,6}*48a
24-fold quotients : {4,4}*32, {8,2}*32
32-fold quotients : {2,6}*24
48-fold quotients : {2,4}*16, {4,2}*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 := ( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,199)( 8,200)
( 9,201)( 10,202)( 11,203)( 12,204)( 13,205)( 14,206)( 15,207)( 16,208)
( 17,209)( 18,210)( 19,211)( 20,212)( 21,213)( 22,214)( 23,215)( 24,216)
( 25,226)( 26,227)( 27,228)( 28,223)( 29,224)( 30,225)( 31,220)( 32,221)
( 33,222)( 34,217)( 35,218)( 36,219)( 37,238)( 38,239)( 39,240)( 40,235)
( 41,236)( 42,237)( 43,232)( 44,233)( 45,234)( 46,229)( 47,230)( 48,231)
( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,259)( 56,260)
( 57,261)( 58,262)( 59,263)( 60,264)( 61,241)( 62,242)( 63,243)( 64,244)
( 65,245)( 66,246)( 67,247)( 68,248)( 69,249)( 70,250)( 71,251)( 72,252)
( 73,286)( 74,287)( 75,288)( 76,283)( 77,284)( 78,285)( 79,280)( 80,281)
( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)( 88,271)
( 89,272)( 90,273)( 91,268)( 92,269)( 93,270)( 94,265)( 95,266)( 96,267)
( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,295)(104,296)
(105,297)(106,298)(107,299)(108,300)(109,301)(110,302)(111,303)(112,304)
(113,305)(114,306)(115,307)(116,308)(117,309)(118,310)(119,311)(120,312)
(121,322)(122,323)(123,324)(124,319)(125,320)(126,321)(127,316)(128,317)
(129,318)(130,313)(131,314)(132,315)(133,334)(134,335)(135,336)(136,331)
(137,332)(138,333)(139,328)(140,329)(141,330)(142,325)(143,326)(144,327)
(145,349)(146,350)(147,351)(148,352)(149,353)(150,354)(151,355)(152,356)
(153,357)(154,358)(155,359)(156,360)(157,337)(158,338)(159,339)(160,340)
(161,341)(162,342)(163,343)(164,344)(165,345)(166,346)(167,347)(168,348)
(169,382)(170,383)(171,384)(172,379)(173,380)(174,381)(175,376)(176,377)
(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)(184,367)
(185,368)(186,369)(187,364)(188,365)(189,366)(190,361)(191,362)(192,363);;
s1 := ( 2, 3)( 5, 6)( 7, 10)( 8, 12)( 9, 11)( 14, 15)( 17, 18)( 19, 22)
( 20, 24)( 21, 23)( 25, 28)( 26, 30)( 27, 29)( 32, 33)( 35, 36)( 37, 40)
( 38, 42)( 39, 41)( 44, 45)( 47, 48)( 49, 61)( 50, 63)( 51, 62)( 52, 64)
( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)( 58, 67)( 59, 69)( 60, 68)
( 73, 88)( 74, 90)( 75, 89)( 76, 85)( 77, 87)( 78, 86)( 79, 91)( 80, 93)
( 81, 92)( 82, 94)( 83, 96)( 84, 95)( 97,121)( 98,123)( 99,122)(100,124)
(101,126)(102,125)(103,130)(104,132)(105,131)(106,127)(107,129)(108,128)
(109,133)(110,135)(111,134)(112,136)(113,138)(114,137)(115,142)(116,144)
(117,143)(118,139)(119,141)(120,140)(145,184)(146,186)(147,185)(148,181)
(149,183)(150,182)(151,187)(152,189)(153,188)(154,190)(155,192)(156,191)
(157,172)(158,174)(159,173)(160,169)(161,171)(162,170)(163,175)(164,177)
(165,176)(166,178)(167,180)(168,179)(193,241)(194,243)(195,242)(196,244)
(197,246)(198,245)(199,250)(200,252)(201,251)(202,247)(203,249)(204,248)
(205,253)(206,255)(207,254)(208,256)(209,258)(210,257)(211,262)(212,264)
(213,263)(214,259)(215,261)(216,260)(217,268)(218,270)(219,269)(220,265)
(221,267)(222,266)(223,271)(224,273)(225,272)(226,274)(227,276)(228,275)
(229,280)(230,282)(231,281)(232,277)(233,279)(234,278)(235,283)(236,285)
(237,284)(238,286)(239,288)(240,287)(289,367)(290,369)(291,368)(292,370)
(293,372)(294,371)(295,364)(296,366)(297,365)(298,361)(299,363)(300,362)
(301,379)(302,381)(303,380)(304,382)(305,384)(306,383)(307,376)(308,378)
(309,377)(310,373)(311,375)(312,374)(313,343)(314,345)(315,344)(316,346)
(317,348)(318,347)(319,340)(320,342)(321,341)(322,337)(323,339)(324,338)
(325,355)(326,357)(327,356)(328,358)(329,360)(330,359)(331,352)(332,354)
(333,353)(334,349)(335,351)(336,350);;
s2 := ( 1, 99)( 2, 98)( 3, 97)( 4,102)( 5,101)( 6,100)( 7,105)( 8,104)
( 9,103)( 10,108)( 11,107)( 12,106)( 13,111)( 14,110)( 15,109)( 16,114)
( 17,113)( 18,112)( 19,117)( 20,116)( 21,115)( 22,120)( 23,119)( 24,118)
( 25,126)( 26,125)( 27,124)( 28,123)( 29,122)( 30,121)( 31,132)( 32,131)
( 33,130)( 34,129)( 35,128)( 36,127)( 37,138)( 38,137)( 39,136)( 40,135)
( 41,134)( 42,133)( 43,144)( 44,143)( 45,142)( 46,141)( 47,140)( 48,139)
( 49,153)( 50,152)( 51,151)( 52,156)( 53,155)( 54,154)( 55,147)( 56,146)
( 57,145)( 58,150)( 59,149)( 60,148)( 61,165)( 62,164)( 63,163)( 64,168)
( 65,167)( 66,166)( 67,159)( 68,158)( 69,157)( 70,162)( 71,161)( 72,160)
( 73,180)( 74,179)( 75,178)( 76,177)( 77,176)( 78,175)( 79,174)( 80,173)
( 81,172)( 82,171)( 83,170)( 84,169)( 85,192)( 86,191)( 87,190)( 88,189)
( 89,188)( 90,187)( 91,186)( 92,185)( 93,184)( 94,183)( 95,182)( 96,181)
(193,291)(194,290)(195,289)(196,294)(197,293)(198,292)(199,297)(200,296)
(201,295)(202,300)(203,299)(204,298)(205,303)(206,302)(207,301)(208,306)
(209,305)(210,304)(211,309)(212,308)(213,307)(214,312)(215,311)(216,310)
(217,318)(218,317)(219,316)(220,315)(221,314)(222,313)(223,324)(224,323)
(225,322)(226,321)(227,320)(228,319)(229,330)(230,329)(231,328)(232,327)
(233,326)(234,325)(235,336)(236,335)(237,334)(238,333)(239,332)(240,331)
(241,345)(242,344)(243,343)(244,348)(245,347)(246,346)(247,339)(248,338)
(249,337)(250,342)(251,341)(252,340)(253,357)(254,356)(255,355)(256,360)
(257,359)(258,358)(259,351)(260,350)(261,349)(262,354)(263,353)(264,352)
(265,372)(266,371)(267,370)(268,369)(269,368)(270,367)(271,366)(272,365)
(273,364)(274,363)(275,362)(276,361)(277,384)(278,383)(279,382)(280,381)
(281,380)(282,379)(283,378)(284,377)(285,376)(286,375)(287,374)(288,373);;
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*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,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,199)
( 8,200)( 9,201)( 10,202)( 11,203)( 12,204)( 13,205)( 14,206)( 15,207)
( 16,208)( 17,209)( 18,210)( 19,211)( 20,212)( 21,213)( 22,214)( 23,215)
( 24,216)( 25,226)( 26,227)( 27,228)( 28,223)( 29,224)( 30,225)( 31,220)
( 32,221)( 33,222)( 34,217)( 35,218)( 36,219)( 37,238)( 38,239)( 39,240)
( 40,235)( 41,236)( 42,237)( 43,232)( 44,233)( 45,234)( 46,229)( 47,230)
( 48,231)( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,259)
( 56,260)( 57,261)( 58,262)( 59,263)( 60,264)( 61,241)( 62,242)( 63,243)
( 64,244)( 65,245)( 66,246)( 67,247)( 68,248)( 69,249)( 70,250)( 71,251)
( 72,252)( 73,286)( 74,287)( 75,288)( 76,283)( 77,284)( 78,285)( 79,280)
( 80,281)( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)
( 88,271)( 89,272)( 90,273)( 91,268)( 92,269)( 93,270)( 94,265)( 95,266)
( 96,267)( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,295)
(104,296)(105,297)(106,298)(107,299)(108,300)(109,301)(110,302)(111,303)
(112,304)(113,305)(114,306)(115,307)(116,308)(117,309)(118,310)(119,311)
(120,312)(121,322)(122,323)(123,324)(124,319)(125,320)(126,321)(127,316)
(128,317)(129,318)(130,313)(131,314)(132,315)(133,334)(134,335)(135,336)
(136,331)(137,332)(138,333)(139,328)(140,329)(141,330)(142,325)(143,326)
(144,327)(145,349)(146,350)(147,351)(148,352)(149,353)(150,354)(151,355)
(152,356)(153,357)(154,358)(155,359)(156,360)(157,337)(158,338)(159,339)
(160,340)(161,341)(162,342)(163,343)(164,344)(165,345)(166,346)(167,347)
(168,348)(169,382)(170,383)(171,384)(172,379)(173,380)(174,381)(175,376)
(176,377)(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)
(184,367)(185,368)(186,369)(187,364)(188,365)(189,366)(190,361)(191,362)
(192,363);
s1 := Sym(384)!( 2, 3)( 5, 6)( 7, 10)( 8, 12)( 9, 11)( 14, 15)( 17, 18)
( 19, 22)( 20, 24)( 21, 23)( 25, 28)( 26, 30)( 27, 29)( 32, 33)( 35, 36)
( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 47, 48)( 49, 61)( 50, 63)( 51, 62)
( 52, 64)( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)( 58, 67)( 59, 69)
( 60, 68)( 73, 88)( 74, 90)( 75, 89)( 76, 85)( 77, 87)( 78, 86)( 79, 91)
( 80, 93)( 81, 92)( 82, 94)( 83, 96)( 84, 95)( 97,121)( 98,123)( 99,122)
(100,124)(101,126)(102,125)(103,130)(104,132)(105,131)(106,127)(107,129)
(108,128)(109,133)(110,135)(111,134)(112,136)(113,138)(114,137)(115,142)
(116,144)(117,143)(118,139)(119,141)(120,140)(145,184)(146,186)(147,185)
(148,181)(149,183)(150,182)(151,187)(152,189)(153,188)(154,190)(155,192)
(156,191)(157,172)(158,174)(159,173)(160,169)(161,171)(162,170)(163,175)
(164,177)(165,176)(166,178)(167,180)(168,179)(193,241)(194,243)(195,242)
(196,244)(197,246)(198,245)(199,250)(200,252)(201,251)(202,247)(203,249)
(204,248)(205,253)(206,255)(207,254)(208,256)(209,258)(210,257)(211,262)
(212,264)(213,263)(214,259)(215,261)(216,260)(217,268)(218,270)(219,269)
(220,265)(221,267)(222,266)(223,271)(224,273)(225,272)(226,274)(227,276)
(228,275)(229,280)(230,282)(231,281)(232,277)(233,279)(234,278)(235,283)
(236,285)(237,284)(238,286)(239,288)(240,287)(289,367)(290,369)(291,368)
(292,370)(293,372)(294,371)(295,364)(296,366)(297,365)(298,361)(299,363)
(300,362)(301,379)(302,381)(303,380)(304,382)(305,384)(306,383)(307,376)
(308,378)(309,377)(310,373)(311,375)(312,374)(313,343)(314,345)(315,344)
(316,346)(317,348)(318,347)(319,340)(320,342)(321,341)(322,337)(323,339)
(324,338)(325,355)(326,357)(327,356)(328,358)(329,360)(330,359)(331,352)
(332,354)(333,353)(334,349)(335,351)(336,350);
s2 := Sym(384)!( 1, 99)( 2, 98)( 3, 97)( 4,102)( 5,101)( 6,100)( 7,105)
( 8,104)( 9,103)( 10,108)( 11,107)( 12,106)( 13,111)( 14,110)( 15,109)
( 16,114)( 17,113)( 18,112)( 19,117)( 20,116)( 21,115)( 22,120)( 23,119)
( 24,118)( 25,126)( 26,125)( 27,124)( 28,123)( 29,122)( 30,121)( 31,132)
( 32,131)( 33,130)( 34,129)( 35,128)( 36,127)( 37,138)( 38,137)( 39,136)
( 40,135)( 41,134)( 42,133)( 43,144)( 44,143)( 45,142)( 46,141)( 47,140)
( 48,139)( 49,153)( 50,152)( 51,151)( 52,156)( 53,155)( 54,154)( 55,147)
( 56,146)( 57,145)( 58,150)( 59,149)( 60,148)( 61,165)( 62,164)( 63,163)
( 64,168)( 65,167)( 66,166)( 67,159)( 68,158)( 69,157)( 70,162)( 71,161)
( 72,160)( 73,180)( 74,179)( 75,178)( 76,177)( 77,176)( 78,175)( 79,174)
( 80,173)( 81,172)( 82,171)( 83,170)( 84,169)( 85,192)( 86,191)( 87,190)
( 88,189)( 89,188)( 90,187)( 91,186)( 92,185)( 93,184)( 94,183)( 95,182)
( 96,181)(193,291)(194,290)(195,289)(196,294)(197,293)(198,292)(199,297)
(200,296)(201,295)(202,300)(203,299)(204,298)(205,303)(206,302)(207,301)
(208,306)(209,305)(210,304)(211,309)(212,308)(213,307)(214,312)(215,311)
(216,310)(217,318)(218,317)(219,316)(220,315)(221,314)(222,313)(223,324)
(224,323)(225,322)(226,321)(227,320)(228,319)(229,330)(230,329)(231,328)
(232,327)(233,326)(234,325)(235,336)(236,335)(237,334)(238,333)(239,332)
(240,331)(241,345)(242,344)(243,343)(244,348)(245,347)(246,346)(247,339)
(248,338)(249,337)(250,342)(251,341)(252,340)(253,357)(254,356)(255,355)
(256,360)(257,359)(258,358)(259,351)(260,350)(261,349)(262,354)(263,353)
(264,352)(265,372)(266,371)(267,370)(268,369)(269,368)(270,367)(271,366)
(272,365)(273,364)(274,363)(275,362)(276,361)(277,384)(278,383)(279,382)
(280,381)(281,380)(282,379)(283,378)(284,377)(285,376)(286,375)(287,374)
(288,373);
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*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,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2 >;
References : None.
to this polytope