Polytope of Type {8,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,24}*768j
if this polytope has a name.
Group : SmallGroup(768,1086593)
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}*384d
4-fold quotients : {4,12}*192b, {8,6}*192b
8-fold quotients : {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
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)
( 97,319)( 98,320)( 99,317)(100,318)(101,316)(102,315)(103,314)(104,313)
(105,327)(106,328)(107,325)(108,326)(109,324)(110,323)(111,322)(112,321)
(113,335)(114,336)(115,333)(116,334)(117,332)(118,331)(119,330)(120,329)
(121,295)(122,296)(123,293)(124,294)(125,292)(126,291)(127,290)(128,289)
(129,303)(130,304)(131,301)(132,302)(133,300)(134,299)(135,298)(136,297)
(137,311)(138,312)(139,309)(140,310)(141,308)(142,307)(143,306)(144,305)
(145,367)(146,368)(147,365)(148,366)(149,364)(150,363)(151,362)(152,361)
(153,375)(154,376)(155,373)(156,374)(157,372)(158,371)(159,370)(160,369)
(161,383)(162,384)(163,381)(164,382)(165,380)(166,379)(167,378)(168,377)
(169,343)(170,344)(171,341)(172,342)(173,340)(174,339)(175,338)(176,337)
(177,351)(178,352)(179,349)(180,350)(181,348)(182,347)(183,346)(184,345)
(185,359)(186,360)(187,357)(188,358)(189,356)(190,355)(191,354)(192,353);;
s1 := ( 1,362)( 2,361)( 3,363)( 4,364)( 5,368)( 6,367)( 7,366)( 8,365)
( 9,378)( 10,377)( 11,379)( 12,380)( 13,384)( 14,383)( 15,382)( 16,381)
( 17,370)( 18,369)( 19,371)( 20,372)( 21,376)( 22,375)( 23,374)( 24,373)
( 25,338)( 26,337)( 27,339)( 28,340)( 29,344)( 30,343)( 31,342)( 32,341)
( 33,354)( 34,353)( 35,355)( 36,356)( 37,360)( 38,359)( 39,358)( 40,357)
( 41,346)( 42,345)( 43,347)( 44,348)( 45,352)( 46,351)( 47,350)( 48,349)
( 49,314)( 50,313)( 51,315)( 52,316)( 53,320)( 54,319)( 55,318)( 56,317)
( 57,330)( 58,329)( 59,331)( 60,332)( 61,336)( 62,335)( 63,334)( 64,333)
( 65,322)( 66,321)( 67,323)( 68,324)( 69,328)( 70,327)( 71,326)( 72,325)
( 73,290)( 74,289)( 75,291)( 76,292)( 77,296)( 78,295)( 79,294)( 80,293)
( 81,306)( 82,305)( 83,307)( 84,308)( 85,312)( 86,311)( 87,310)( 88,309)
( 89,298)( 90,297)( 91,299)( 92,300)( 93,304)( 94,303)( 95,302)( 96,301)
( 97,266)( 98,265)( 99,267)(100,268)(101,272)(102,271)(103,270)(104,269)
(105,282)(106,281)(107,283)(108,284)(109,288)(110,287)(111,286)(112,285)
(113,274)(114,273)(115,275)(116,276)(117,280)(118,279)(119,278)(120,277)
(121,242)(122,241)(123,243)(124,244)(125,248)(126,247)(127,246)(128,245)
(129,258)(130,257)(131,259)(132,260)(133,264)(134,263)(135,262)(136,261)
(137,250)(138,249)(139,251)(140,252)(141,256)(142,255)(143,254)(144,253)
(145,218)(146,217)(147,219)(148,220)(149,224)(150,223)(151,222)(152,221)
(153,234)(154,233)(155,235)(156,236)(157,240)(158,239)(159,238)(160,237)
(161,226)(162,225)(163,227)(164,228)(165,232)(166,231)(167,230)(168,229)
(169,194)(170,193)(171,195)(172,196)(173,200)(174,199)(175,198)(176,197)
(177,210)(178,209)(179,211)(180,212)(181,216)(182,215)(183,214)(184,213)
(185,202)(186,201)(187,203)(188,204)(189,208)(190,207)(191,206)(192,205);;
s2 := ( 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)(193,210)(194,209)
(195,213)(196,214)(197,211)(198,212)(199,215)(200,216)(201,202)(203,205)
(204,206)(217,234)(218,233)(219,237)(220,238)(221,235)(222,236)(223,239)
(224,240)(225,226)(227,229)(228,230)(241,282)(242,281)(243,285)(244,286)
(245,283)(246,284)(247,287)(248,288)(249,274)(250,273)(251,277)(252,278)
(253,275)(254,276)(255,279)(256,280)(257,266)(258,265)(259,269)(260,270)
(261,267)(262,268)(263,271)(264,272)(289,354)(290,353)(291,357)(292,358)
(293,355)(294,356)(295,359)(296,360)(297,346)(298,345)(299,349)(300,350)
(301,347)(302,348)(303,351)(304,352)(305,338)(306,337)(307,341)(308,342)
(309,339)(310,340)(311,343)(312,344)(313,378)(314,377)(315,381)(316,382)
(317,379)(318,380)(319,383)(320,384)(321,370)(322,369)(323,373)(324,374)
(325,371)(326,372)(327,375)(328,376)(329,362)(330,361)(331,365)(332,366)
(333,363)(334,364)(335,367)(336,368);;
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,
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 ];;
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)( 97,319)( 98,320)( 99,317)(100,318)(101,316)(102,315)(103,314)
(104,313)(105,327)(106,328)(107,325)(108,326)(109,324)(110,323)(111,322)
(112,321)(113,335)(114,336)(115,333)(116,334)(117,332)(118,331)(119,330)
(120,329)(121,295)(122,296)(123,293)(124,294)(125,292)(126,291)(127,290)
(128,289)(129,303)(130,304)(131,301)(132,302)(133,300)(134,299)(135,298)
(136,297)(137,311)(138,312)(139,309)(140,310)(141,308)(142,307)(143,306)
(144,305)(145,367)(146,368)(147,365)(148,366)(149,364)(150,363)(151,362)
(152,361)(153,375)(154,376)(155,373)(156,374)(157,372)(158,371)(159,370)
(160,369)(161,383)(162,384)(163,381)(164,382)(165,380)(166,379)(167,378)
(168,377)(169,343)(170,344)(171,341)(172,342)(173,340)(174,339)(175,338)
(176,337)(177,351)(178,352)(179,349)(180,350)(181,348)(182,347)(183,346)
(184,345)(185,359)(186,360)(187,357)(188,358)(189,356)(190,355)(191,354)
(192,353);
s1 := Sym(384)!( 1,362)( 2,361)( 3,363)( 4,364)( 5,368)( 6,367)( 7,366)
( 8,365)( 9,378)( 10,377)( 11,379)( 12,380)( 13,384)( 14,383)( 15,382)
( 16,381)( 17,370)( 18,369)( 19,371)( 20,372)( 21,376)( 22,375)( 23,374)
( 24,373)( 25,338)( 26,337)( 27,339)( 28,340)( 29,344)( 30,343)( 31,342)
( 32,341)( 33,354)( 34,353)( 35,355)( 36,356)( 37,360)( 38,359)( 39,358)
( 40,357)( 41,346)( 42,345)( 43,347)( 44,348)( 45,352)( 46,351)( 47,350)
( 48,349)( 49,314)( 50,313)( 51,315)( 52,316)( 53,320)( 54,319)( 55,318)
( 56,317)( 57,330)( 58,329)( 59,331)( 60,332)( 61,336)( 62,335)( 63,334)
( 64,333)( 65,322)( 66,321)( 67,323)( 68,324)( 69,328)( 70,327)( 71,326)
( 72,325)( 73,290)( 74,289)( 75,291)( 76,292)( 77,296)( 78,295)( 79,294)
( 80,293)( 81,306)( 82,305)( 83,307)( 84,308)( 85,312)( 86,311)( 87,310)
( 88,309)( 89,298)( 90,297)( 91,299)( 92,300)( 93,304)( 94,303)( 95,302)
( 96,301)( 97,266)( 98,265)( 99,267)(100,268)(101,272)(102,271)(103,270)
(104,269)(105,282)(106,281)(107,283)(108,284)(109,288)(110,287)(111,286)
(112,285)(113,274)(114,273)(115,275)(116,276)(117,280)(118,279)(119,278)
(120,277)(121,242)(122,241)(123,243)(124,244)(125,248)(126,247)(127,246)
(128,245)(129,258)(130,257)(131,259)(132,260)(133,264)(134,263)(135,262)
(136,261)(137,250)(138,249)(139,251)(140,252)(141,256)(142,255)(143,254)
(144,253)(145,218)(146,217)(147,219)(148,220)(149,224)(150,223)(151,222)
(152,221)(153,234)(154,233)(155,235)(156,236)(157,240)(158,239)(159,238)
(160,237)(161,226)(162,225)(163,227)(164,228)(165,232)(166,231)(167,230)
(168,229)(169,194)(170,193)(171,195)(172,196)(173,200)(174,199)(175,198)
(176,197)(177,210)(178,209)(179,211)(180,212)(181,216)(182,215)(183,214)
(184,213)(185,202)(186,201)(187,203)(188,204)(189,208)(190,207)(191,206)
(192,205);
s2 := 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)(193,210)
(194,209)(195,213)(196,214)(197,211)(198,212)(199,215)(200,216)(201,202)
(203,205)(204,206)(217,234)(218,233)(219,237)(220,238)(221,235)(222,236)
(223,239)(224,240)(225,226)(227,229)(228,230)(241,282)(242,281)(243,285)
(244,286)(245,283)(246,284)(247,287)(248,288)(249,274)(250,273)(251,277)
(252,278)(253,275)(254,276)(255,279)(256,280)(257,266)(258,265)(259,269)
(260,270)(261,267)(262,268)(263,271)(264,272)(289,354)(290,353)(291,357)
(292,358)(293,355)(294,356)(295,359)(296,360)(297,346)(298,345)(299,349)
(300,350)(301,347)(302,348)(303,351)(304,352)(305,338)(306,337)(307,341)
(308,342)(309,339)(310,340)(311,343)(312,344)(313,378)(314,377)(315,381)
(316,382)(317,379)(318,380)(319,383)(320,384)(321,370)(322,369)(323,373)
(324,374)(325,371)(326,372)(327,375)(328,376)(329,362)(330,361)(331,365)
(332,366)(333,363)(334,364)(335,367)(336,368);
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,
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 >;
References : None.
to this polytope