Polytope of Type {8,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,24}*768a
if this polytope has a name.
Group : SmallGroup(768,58267)
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 : {4,24}*384a, {8,24}*384a, {8,24}*384b, {8,12}*384a, {8,24}*384c, {8,24}*384d
   3-fold quotients : {8,8}*256a
   4-fold quotients : {4,24}*192a, {4,12}*192a, {4,24}*192b, {8,12}*192a, {8,12}*192b
   6-fold quotients : {4,8}*128a, {8,4}*128a, {8,8}*128a, {8,8}*128b, {8,8}*128c, {8,8}*128d
   8-fold quotients : {4,12}*96a, {2,24}*96, {8,6}*96
   12-fold quotients : {4,8}*64a, {8,4}*64a, {4,8}*64b, {8,4}*64b, {4,4}*64
   16-fold quotients : {2,12}*48, {4,6}*48a
   24-fold quotients : {4,4}*32, {2,8}*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)
( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,217)( 32,218)
( 33,219)( 34,220)( 35,221)( 36,222)( 37,235)( 38,236)( 39,237)( 40,238)
( 41,239)( 42,240)( 43,229)( 44,230)( 45,231)( 46,232)( 47,233)( 48,234)
( 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)
( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,277)( 80,278)
( 81,279)( 82,280)( 83,281)( 84,282)( 85,271)( 86,272)( 87,273)( 88,274)
( 89,275)( 90,276)( 91,265)( 92,266)( 93,267)( 94,268)( 95,269)( 96,270)
( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,295)(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)
(121,319)(122,320)(123,321)(124,322)(125,323)(126,324)(127,313)(128,314)
(129,315)(130,316)(131,317)(132,318)(133,331)(134,332)(135,333)(136,334)
(137,335)(138,336)(139,325)(140,326)(141,327)(142,328)(143,329)(144,330)
(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)
(169,379)(170,380)(171,381)(172,382)(173,383)(174,384)(175,373)(176,374)
(177,375)(178,376)(179,377)(180,378)(181,367)(182,368)(183,369)(184,370)
(185,371)(186,372)(187,361)(188,362)(189,363)(190,364)(191,365)(192,366);;
s1 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 25, 28)( 26, 30)( 27, 29)( 31, 34)( 32, 36)( 33, 35)( 37, 40)( 38, 42)
( 39, 41)( 43, 46)( 44, 48)( 45, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 64)
( 53, 66)( 54, 65)( 55, 67)( 56, 69)( 57, 68)( 58, 70)( 59, 72)( 60, 71)
( 73, 88)( 74, 90)( 75, 89)( 76, 85)( 77, 87)( 78, 86)( 79, 94)( 80, 96)
( 81, 95)( 82, 91)( 83, 93)( 84, 92)( 97,121)( 98,123)( 99,122)(100,124)
(101,126)(102,125)(103,127)(104,129)(105,128)(106,130)(107,132)(108,131)
(109,133)(110,135)(111,134)(112,136)(113,138)(114,137)(115,139)(116,141)
(117,140)(118,142)(119,144)(120,143)(145,181)(146,183)(147,182)(148,184)
(149,186)(150,185)(151,187)(152,189)(153,188)(154,190)(155,192)(156,191)
(157,169)(158,171)(159,170)(160,172)(161,174)(162,173)(163,175)(164,177)
(165,176)(166,178)(167,180)(168,179)(193,241)(194,243)(195,242)(196,244)
(197,246)(198,245)(199,247)(200,249)(201,248)(202,250)(203,252)(204,251)
(205,253)(206,255)(207,254)(208,256)(209,258)(210,257)(211,259)(212,261)
(213,260)(214,262)(215,264)(216,263)(217,268)(218,270)(219,269)(220,265)
(221,267)(222,266)(223,274)(224,276)(225,275)(226,271)(227,273)(228,272)
(229,280)(230,282)(231,281)(232,277)(233,279)(234,278)(235,286)(236,288)
(237,287)(238,283)(239,285)(240,284)(289,367)(290,369)(291,368)(292,370)
(293,372)(294,371)(295,361)(296,363)(297,362)(298,364)(299,366)(300,365)
(301,379)(302,381)(303,380)(304,382)(305,384)(306,383)(307,373)(308,375)
(309,374)(310,376)(311,378)(312,377)(313,343)(314,345)(315,344)(316,346)
(317,348)(318,347)(319,337)(320,339)(321,338)(322,340)(323,342)(324,341)
(325,355)(326,357)(327,356)(328,358)(329,360)(330,359)(331,349)(332,351)
(333,350)(334,352)(335,354)(336,353);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*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)!(  1,193)(  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)( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,217)
( 32,218)( 33,219)( 34,220)( 35,221)( 36,222)( 37,235)( 38,236)( 39,237)
( 40,238)( 41,239)( 42,240)( 43,229)( 44,230)( 45,231)( 46,232)( 47,233)
( 48,234)( 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)( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,277)
( 80,278)( 81,279)( 82,280)( 83,281)( 84,282)( 85,271)( 86,272)( 87,273)
( 88,274)( 89,275)( 90,276)( 91,265)( 92,266)( 93,267)( 94,268)( 95,269)
( 96,270)( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,295)
(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)(121,319)(122,320)(123,321)(124,322)(125,323)(126,324)(127,313)
(128,314)(129,315)(130,316)(131,317)(132,318)(133,331)(134,332)(135,333)
(136,334)(137,335)(138,336)(139,325)(140,326)(141,327)(142,328)(143,329)
(144,330)(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)(169,379)(170,380)(171,381)(172,382)(173,383)(174,384)(175,373)
(176,374)(177,375)(178,376)(179,377)(180,378)(181,367)(182,368)(183,369)
(184,370)(185,371)(186,372)(187,361)(188,362)(189,363)(190,364)(191,365)
(192,366);
s1 := Sym(384)!(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)
( 23, 24)( 25, 28)( 26, 30)( 27, 29)( 31, 34)( 32, 36)( 33, 35)( 37, 40)
( 38, 42)( 39, 41)( 43, 46)( 44, 48)( 45, 47)( 49, 61)( 50, 63)( 51, 62)
( 52, 64)( 53, 66)( 54, 65)( 55, 67)( 56, 69)( 57, 68)( 58, 70)( 59, 72)
( 60, 71)( 73, 88)( 74, 90)( 75, 89)( 76, 85)( 77, 87)( 78, 86)( 79, 94)
( 80, 96)( 81, 95)( 82, 91)( 83, 93)( 84, 92)( 97,121)( 98,123)( 99,122)
(100,124)(101,126)(102,125)(103,127)(104,129)(105,128)(106,130)(107,132)
(108,131)(109,133)(110,135)(111,134)(112,136)(113,138)(114,137)(115,139)
(116,141)(117,140)(118,142)(119,144)(120,143)(145,181)(146,183)(147,182)
(148,184)(149,186)(150,185)(151,187)(152,189)(153,188)(154,190)(155,192)
(156,191)(157,169)(158,171)(159,170)(160,172)(161,174)(162,173)(163,175)
(164,177)(165,176)(166,178)(167,180)(168,179)(193,241)(194,243)(195,242)
(196,244)(197,246)(198,245)(199,247)(200,249)(201,248)(202,250)(203,252)
(204,251)(205,253)(206,255)(207,254)(208,256)(209,258)(210,257)(211,259)
(212,261)(213,260)(214,262)(215,264)(216,263)(217,268)(218,270)(219,269)
(220,265)(221,267)(222,266)(223,274)(224,276)(225,275)(226,271)(227,273)
(228,272)(229,280)(230,282)(231,281)(232,277)(233,279)(234,278)(235,286)
(236,288)(237,287)(238,283)(239,285)(240,284)(289,367)(290,369)(291,368)
(292,370)(293,372)(294,371)(295,361)(296,363)(297,362)(298,364)(299,366)
(300,365)(301,379)(302,381)(303,380)(304,382)(305,384)(306,383)(307,373)
(308,375)(309,374)(310,376)(311,378)(312,377)(313,343)(314,345)(315,344)
(316,346)(317,348)(318,347)(319,337)(320,339)(321,338)(322,340)(323,342)
(324,341)(325,355)(326,357)(327,356)(328,358)(329,360)(330,359)(331,349)
(332,351)(333,350)(334,352)(335,354)(336,353);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*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