Polytope of Type {24,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*768l
if this polytope has a name.
Group : SmallGroup(768,1086641)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 48, 192, 16
Order of s0s1s2 : 24
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,8}*384f, {24,4}*384d
4-fold quotients : {12,4}*192b, {6,8}*192c
8-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
16-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
32-fold quotients : {3,4}*24, {6,2}*24
48-fold quotients : {4,2}*16
64-fold quotients : {3,2}*12
96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 1,377)( 2,378)( 3,382)( 4,381)( 5,380)( 6,379)( 7,384)( 8,383)
( 9,369)( 10,370)( 11,374)( 12,373)( 13,372)( 14,371)( 15,376)( 16,375)
( 17,361)( 18,362)( 19,366)( 20,365)( 21,364)( 22,363)( 23,368)( 24,367)
( 25,353)( 26,354)( 27,358)( 28,357)( 29,356)( 30,355)( 31,360)( 32,359)
( 33,345)( 34,346)( 35,350)( 36,349)( 37,348)( 38,347)( 39,352)( 40,351)
( 41,337)( 42,338)( 43,342)( 44,341)( 45,340)( 46,339)( 47,344)( 48,343)
( 49,329)( 50,330)( 51,334)( 52,333)( 53,332)( 54,331)( 55,336)( 56,335)
( 57,321)( 58,322)( 59,326)( 60,325)( 61,324)( 62,323)( 63,328)( 64,327)
( 65,313)( 66,314)( 67,318)( 68,317)( 69,316)( 70,315)( 71,320)( 72,319)
( 73,305)( 74,306)( 75,310)( 76,309)( 77,308)( 78,307)( 79,312)( 80,311)
( 81,297)( 82,298)( 83,302)( 84,301)( 85,300)( 86,299)( 87,304)( 88,303)
( 89,289)( 90,290)( 91,294)( 92,293)( 93,292)( 94,291)( 95,296)( 96,295)
( 97,281)( 98,282)( 99,286)(100,285)(101,284)(102,283)(103,288)(104,287)
(105,273)(106,274)(107,278)(108,277)(109,276)(110,275)(111,280)(112,279)
(113,265)(114,266)(115,270)(116,269)(117,268)(118,267)(119,272)(120,271)
(121,257)(122,258)(123,262)(124,261)(125,260)(126,259)(127,264)(128,263)
(129,249)(130,250)(131,254)(132,253)(133,252)(134,251)(135,256)(136,255)
(137,241)(138,242)(139,246)(140,245)(141,244)(142,243)(143,248)(144,247)
(145,233)(146,234)(147,238)(148,237)(149,236)(150,235)(151,240)(152,239)
(153,225)(154,226)(155,230)(156,229)(157,228)(158,227)(159,232)(160,231)
(161,217)(162,218)(163,222)(164,221)(165,220)(166,219)(167,224)(168,223)
(169,209)(170,210)(171,214)(172,213)(173,212)(174,211)(175,216)(176,215)
(177,201)(178,202)(179,206)(180,205)(181,204)(182,203)(183,208)(184,207)
(185,193)(186,194)(187,198)(188,197)(189,196)(190,195)(191,200)(192,199);;
s2 := ( 1,196)( 2,195)( 3,193)( 4,194)( 5,200)( 6,199)( 7,197)( 8,198)
( 9,204)( 10,203)( 11,201)( 12,202)( 13,208)( 14,207)( 15,205)( 16,206)
( 17,212)( 18,211)( 19,209)( 20,210)( 21,216)( 22,215)( 23,213)( 24,214)
( 25,220)( 26,219)( 27,217)( 28,218)( 29,224)( 30,223)( 31,221)( 32,222)
( 33,228)( 34,227)( 35,225)( 36,226)( 37,232)( 38,231)( 39,229)( 40,230)
( 41,236)( 42,235)( 43,233)( 44,234)( 45,240)( 46,239)( 47,237)( 48,238)
( 49,244)( 50,243)( 51,241)( 52,242)( 53,248)( 54,247)( 55,245)( 56,246)
( 57,252)( 58,251)( 59,249)( 60,250)( 61,256)( 62,255)( 63,253)( 64,254)
( 65,260)( 66,259)( 67,257)( 68,258)( 69,264)( 70,263)( 71,261)( 72,262)
( 73,268)( 74,267)( 75,265)( 76,266)( 77,272)( 78,271)( 79,269)( 80,270)
( 81,276)( 82,275)( 83,273)( 84,274)( 85,280)( 86,279)( 87,277)( 88,278)
( 89,284)( 90,283)( 91,281)( 92,282)( 93,288)( 94,287)( 95,285)( 96,286)
( 97,315)( 98,316)( 99,314)(100,313)(101,319)(102,320)(103,318)(104,317)
(105,323)(106,324)(107,322)(108,321)(109,327)(110,328)(111,326)(112,325)
(113,331)(114,332)(115,330)(116,329)(117,335)(118,336)(119,334)(120,333)
(121,291)(122,292)(123,290)(124,289)(125,295)(126,296)(127,294)(128,293)
(129,299)(130,300)(131,298)(132,297)(133,303)(134,304)(135,302)(136,301)
(137,307)(138,308)(139,306)(140,305)(141,311)(142,312)(143,310)(144,309)
(145,363)(146,364)(147,362)(148,361)(149,367)(150,368)(151,366)(152,365)
(153,371)(154,372)(155,370)(156,369)(157,375)(158,376)(159,374)(160,373)
(161,379)(162,380)(163,378)(164,377)(165,383)(166,384)(167,382)(168,381)
(169,339)(170,340)(171,338)(172,337)(173,343)(174,344)(175,342)(176,341)
(177,347)(178,348)(179,346)(180,345)(181,351)(182,352)(183,350)(184,349)
(185,355)(186,356)(187,354)(188,353)(189,359)(190,360)(191,358)(192,357);;
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*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(384)!( 1,377)( 2,378)( 3,382)( 4,381)( 5,380)( 6,379)( 7,384)
( 8,383)( 9,369)( 10,370)( 11,374)( 12,373)( 13,372)( 14,371)( 15,376)
( 16,375)( 17,361)( 18,362)( 19,366)( 20,365)( 21,364)( 22,363)( 23,368)
( 24,367)( 25,353)( 26,354)( 27,358)( 28,357)( 29,356)( 30,355)( 31,360)
( 32,359)( 33,345)( 34,346)( 35,350)( 36,349)( 37,348)( 38,347)( 39,352)
( 40,351)( 41,337)( 42,338)( 43,342)( 44,341)( 45,340)( 46,339)( 47,344)
( 48,343)( 49,329)( 50,330)( 51,334)( 52,333)( 53,332)( 54,331)( 55,336)
( 56,335)( 57,321)( 58,322)( 59,326)( 60,325)( 61,324)( 62,323)( 63,328)
( 64,327)( 65,313)( 66,314)( 67,318)( 68,317)( 69,316)( 70,315)( 71,320)
( 72,319)( 73,305)( 74,306)( 75,310)( 76,309)( 77,308)( 78,307)( 79,312)
( 80,311)( 81,297)( 82,298)( 83,302)( 84,301)( 85,300)( 86,299)( 87,304)
( 88,303)( 89,289)( 90,290)( 91,294)( 92,293)( 93,292)( 94,291)( 95,296)
( 96,295)( 97,281)( 98,282)( 99,286)(100,285)(101,284)(102,283)(103,288)
(104,287)(105,273)(106,274)(107,278)(108,277)(109,276)(110,275)(111,280)
(112,279)(113,265)(114,266)(115,270)(116,269)(117,268)(118,267)(119,272)
(120,271)(121,257)(122,258)(123,262)(124,261)(125,260)(126,259)(127,264)
(128,263)(129,249)(130,250)(131,254)(132,253)(133,252)(134,251)(135,256)
(136,255)(137,241)(138,242)(139,246)(140,245)(141,244)(142,243)(143,248)
(144,247)(145,233)(146,234)(147,238)(148,237)(149,236)(150,235)(151,240)
(152,239)(153,225)(154,226)(155,230)(156,229)(157,228)(158,227)(159,232)
(160,231)(161,217)(162,218)(163,222)(164,221)(165,220)(166,219)(167,224)
(168,223)(169,209)(170,210)(171,214)(172,213)(173,212)(174,211)(175,216)
(176,215)(177,201)(178,202)(179,206)(180,205)(181,204)(182,203)(183,208)
(184,207)(185,193)(186,194)(187,198)(188,197)(189,196)(190,195)(191,200)
(192,199);
s2 := Sym(384)!( 1,196)( 2,195)( 3,193)( 4,194)( 5,200)( 6,199)( 7,197)
( 8,198)( 9,204)( 10,203)( 11,201)( 12,202)( 13,208)( 14,207)( 15,205)
( 16,206)( 17,212)( 18,211)( 19,209)( 20,210)( 21,216)( 22,215)( 23,213)
( 24,214)( 25,220)( 26,219)( 27,217)( 28,218)( 29,224)( 30,223)( 31,221)
( 32,222)( 33,228)( 34,227)( 35,225)( 36,226)( 37,232)( 38,231)( 39,229)
( 40,230)( 41,236)( 42,235)( 43,233)( 44,234)( 45,240)( 46,239)( 47,237)
( 48,238)( 49,244)( 50,243)( 51,241)( 52,242)( 53,248)( 54,247)( 55,245)
( 56,246)( 57,252)( 58,251)( 59,249)( 60,250)( 61,256)( 62,255)( 63,253)
( 64,254)( 65,260)( 66,259)( 67,257)( 68,258)( 69,264)( 70,263)( 71,261)
( 72,262)( 73,268)( 74,267)( 75,265)( 76,266)( 77,272)( 78,271)( 79,269)
( 80,270)( 81,276)( 82,275)( 83,273)( 84,274)( 85,280)( 86,279)( 87,277)
( 88,278)( 89,284)( 90,283)( 91,281)( 92,282)( 93,288)( 94,287)( 95,285)
( 96,286)( 97,315)( 98,316)( 99,314)(100,313)(101,319)(102,320)(103,318)
(104,317)(105,323)(106,324)(107,322)(108,321)(109,327)(110,328)(111,326)
(112,325)(113,331)(114,332)(115,330)(116,329)(117,335)(118,336)(119,334)
(120,333)(121,291)(122,292)(123,290)(124,289)(125,295)(126,296)(127,294)
(128,293)(129,299)(130,300)(131,298)(132,297)(133,303)(134,304)(135,302)
(136,301)(137,307)(138,308)(139,306)(140,305)(141,311)(142,312)(143,310)
(144,309)(145,363)(146,364)(147,362)(148,361)(149,367)(150,368)(151,366)
(152,365)(153,371)(154,372)(155,370)(156,369)(157,375)(158,376)(159,374)
(160,373)(161,379)(162,380)(163,378)(164,377)(165,383)(166,384)(167,382)
(168,381)(169,339)(170,340)(171,338)(172,337)(173,343)(174,344)(175,342)
(176,341)(177,347)(178,348)(179,346)(180,345)(181,351)(182,352)(183,350)
(184,349)(185,355)(186,356)(187,354)(188,353)(189,359)(190,360)(191,358)
(192,357);
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*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 >;
References : None.
to this polytope