Polytope of Type {24,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*768e
if this polytope has a name.
Group : SmallGroup(768,90301)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 48, 192, 16
Order of s0s1s2 : 12
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {24,4}*384b
3-fold quotients : {8,8}*256f
4-fold quotients : {12,4}*192a
6-fold quotients : {8,4}*128b
8-fold quotients : {12,4}*96a
12-fold quotients : {4,4}*64
16-fold quotients : {12,2}*48, {6,4}*48a
24-fold quotients : {4,4}*32
32-fold quotients : {6,2}*24
48-fold quotients : {2,4}*16, {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 := ( 1,289)( 2,291)( 3,290)( 4,292)( 5,294)( 6,293)( 7,295)( 8,297)
( 9,296)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)( 16,301)
( 17,303)( 18,302)( 19,310)( 20,312)( 21,311)( 22,307)( 23,309)( 24,308)
( 25,334)( 26,336)( 27,335)( 28,331)( 29,333)( 30,332)( 31,328)( 32,330)
( 33,329)( 34,325)( 35,327)( 36,326)( 37,322)( 38,324)( 39,323)( 40,319)
( 41,321)( 42,320)( 43,316)( 44,318)( 45,317)( 46,313)( 47,315)( 48,314)
( 49,352)( 50,354)( 51,353)( 52,349)( 53,351)( 54,350)( 55,358)( 56,360)
( 57,359)( 58,355)( 59,357)( 60,356)( 61,340)( 62,342)( 63,341)( 64,337)
( 65,339)( 66,338)( 67,346)( 68,348)( 69,347)( 70,343)( 71,345)( 72,344)
( 73,367)( 74,369)( 75,368)( 76,370)( 77,372)( 78,371)( 79,361)( 80,363)
( 81,362)( 82,364)( 83,366)( 84,365)( 85,382)( 86,384)( 87,383)( 88,379)
( 89,381)( 90,380)( 91,376)( 92,378)( 93,377)( 94,373)( 95,375)( 96,374)
( 97,193)( 98,195)( 99,194)(100,196)(101,198)(102,197)(103,199)(104,201)
(105,200)(106,202)(107,204)(108,203)(109,208)(110,210)(111,209)(112,205)
(113,207)(114,206)(115,214)(116,216)(117,215)(118,211)(119,213)(120,212)
(121,238)(122,240)(123,239)(124,235)(125,237)(126,236)(127,232)(128,234)
(129,233)(130,229)(131,231)(132,230)(133,226)(134,228)(135,227)(136,223)
(137,225)(138,224)(139,220)(140,222)(141,221)(142,217)(143,219)(144,218)
(145,256)(146,258)(147,257)(148,253)(149,255)(150,254)(151,262)(152,264)
(153,263)(154,259)(155,261)(156,260)(157,244)(158,246)(159,245)(160,241)
(161,243)(162,242)(163,250)(164,252)(165,251)(166,247)(167,249)(168,248)
(169,271)(170,273)(171,272)(172,274)(173,276)(174,275)(175,265)(176,267)
(177,266)(178,268)(179,270)(180,269)(181,286)(182,288)(183,287)(184,283)
(185,285)(186,284)(187,280)(188,282)(189,281)(190,277)(191,279)(192,278);;
s1 := ( 1, 3)( 4, 6)( 7, 9)( 10, 12)( 13, 21)( 14, 20)( 15, 19)( 16, 24)
( 17, 23)( 18, 22)( 25, 27)( 28, 30)( 31, 33)( 34, 36)( 37, 45)( 38, 44)
( 39, 43)( 40, 48)( 41, 47)( 42, 46)( 49, 54)( 50, 53)( 51, 52)( 55, 60)
( 56, 59)( 57, 58)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)( 66, 67)
( 73, 78)( 74, 77)( 75, 76)( 79, 84)( 80, 83)( 81, 82)( 85, 96)( 86, 95)
( 87, 94)( 88, 93)( 89, 92)( 90, 91)( 97,123)( 98,122)( 99,121)(100,126)
(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)(107,131)(108,130)
(109,141)(110,140)(111,139)(112,144)(113,143)(114,142)(115,135)(116,134)
(117,133)(118,138)(119,137)(120,136)(145,177)(146,176)(147,175)(148,180)
(149,179)(150,178)(151,171)(152,170)(153,169)(154,174)(155,173)(156,172)
(157,183)(158,182)(159,181)(160,186)(161,185)(162,184)(163,189)(164,188)
(165,187)(166,192)(167,191)(168,190)(193,243)(194,242)(195,241)(196,246)
(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)(203,251)(204,250)
(205,261)(206,260)(207,259)(208,264)(209,263)(210,262)(211,255)(212,254)
(213,253)(214,258)(215,257)(216,256)(217,267)(218,266)(219,265)(220,270)
(221,269)(222,268)(223,273)(224,272)(225,271)(226,276)(227,275)(228,274)
(229,285)(230,284)(231,283)(232,288)(233,287)(234,286)(235,279)(236,278)
(237,277)(238,282)(239,281)(240,280)(289,378)(290,377)(291,376)(292,375)
(293,374)(294,373)(295,384)(296,383)(297,382)(298,381)(299,380)(300,379)
(301,369)(302,368)(303,367)(304,372)(305,371)(306,370)(307,363)(308,362)
(309,361)(310,366)(311,365)(312,364)(313,351)(314,350)(315,349)(316,354)
(317,353)(318,352)(319,357)(320,356)(321,355)(322,360)(323,359)(324,358)
(325,348)(326,347)(327,346)(328,345)(329,344)(330,343)(331,342)(332,341)
(333,340)(334,339)(335,338)(336,337);;
s2 := ( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,202)( 8,203)
( 9,204)( 10,199)( 11,200)( 12,201)( 13,205)( 14,206)( 15,207)( 16,208)
( 17,209)( 18,210)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)( 24,213)
( 25,238)( 26,239)( 27,240)( 28,235)( 29,236)( 30,237)( 31,229)( 32,230)
( 33,231)( 34,232)( 35,233)( 36,234)( 37,223)( 38,224)( 39,225)( 40,226)
( 41,227)( 42,228)( 43,220)( 44,221)( 45,222)( 46,217)( 47,218)( 48,219)
( 49,244)( 50,245)( 51,246)( 52,241)( 53,242)( 54,243)( 55,247)( 56,248)
( 57,249)( 58,250)( 59,251)( 60,252)( 61,256)( 62,257)( 63,258)( 64,253)
( 65,254)( 66,255)( 67,259)( 68,260)( 69,261)( 70,262)( 71,263)( 72,264)
( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,280)( 80,281)
( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)( 88,271)
( 89,272)( 90,273)( 91,265)( 92,266)( 93,267)( 94,268)( 95,269)( 96,270)
( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)(104,299)
(105,300)(106,295)(107,296)(108,297)(109,301)(110,302)(111,303)(112,304)
(113,305)(114,306)(115,310)(116,311)(117,312)(118,307)(119,308)(120,309)
(121,334)(122,335)(123,336)(124,331)(125,332)(126,333)(127,325)(128,326)
(129,327)(130,328)(131,329)(132,330)(133,319)(134,320)(135,321)(136,322)
(137,323)(138,324)(139,316)(140,317)(141,318)(142,313)(143,314)(144,315)
(145,340)(146,341)(147,342)(148,337)(149,338)(150,339)(151,343)(152,344)
(153,345)(154,346)(155,347)(156,348)(157,352)(158,353)(159,354)(160,349)
(161,350)(162,351)(163,355)(164,356)(165,357)(166,358)(167,359)(168,360)
(169,379)(170,380)(171,381)(172,382)(173,383)(174,384)(175,376)(176,377)
(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)(184,367)
(185,368)(186,369)(187,361)(188,362)(189,363)(190,364)(191,365)(192,366);;
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*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1,289)( 2,291)( 3,290)( 4,292)( 5,294)( 6,293)( 7,295)
( 8,297)( 9,296)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)
( 16,301)( 17,303)( 18,302)( 19,310)( 20,312)( 21,311)( 22,307)( 23,309)
( 24,308)( 25,334)( 26,336)( 27,335)( 28,331)( 29,333)( 30,332)( 31,328)
( 32,330)( 33,329)( 34,325)( 35,327)( 36,326)( 37,322)( 38,324)( 39,323)
( 40,319)( 41,321)( 42,320)( 43,316)( 44,318)( 45,317)( 46,313)( 47,315)
( 48,314)( 49,352)( 50,354)( 51,353)( 52,349)( 53,351)( 54,350)( 55,358)
( 56,360)( 57,359)( 58,355)( 59,357)( 60,356)( 61,340)( 62,342)( 63,341)
( 64,337)( 65,339)( 66,338)( 67,346)( 68,348)( 69,347)( 70,343)( 71,345)
( 72,344)( 73,367)( 74,369)( 75,368)( 76,370)( 77,372)( 78,371)( 79,361)
( 80,363)( 81,362)( 82,364)( 83,366)( 84,365)( 85,382)( 86,384)( 87,383)
( 88,379)( 89,381)( 90,380)( 91,376)( 92,378)( 93,377)( 94,373)( 95,375)
( 96,374)( 97,193)( 98,195)( 99,194)(100,196)(101,198)(102,197)(103,199)
(104,201)(105,200)(106,202)(107,204)(108,203)(109,208)(110,210)(111,209)
(112,205)(113,207)(114,206)(115,214)(116,216)(117,215)(118,211)(119,213)
(120,212)(121,238)(122,240)(123,239)(124,235)(125,237)(126,236)(127,232)
(128,234)(129,233)(130,229)(131,231)(132,230)(133,226)(134,228)(135,227)
(136,223)(137,225)(138,224)(139,220)(140,222)(141,221)(142,217)(143,219)
(144,218)(145,256)(146,258)(147,257)(148,253)(149,255)(150,254)(151,262)
(152,264)(153,263)(154,259)(155,261)(156,260)(157,244)(158,246)(159,245)
(160,241)(161,243)(162,242)(163,250)(164,252)(165,251)(166,247)(167,249)
(168,248)(169,271)(170,273)(171,272)(172,274)(173,276)(174,275)(175,265)
(176,267)(177,266)(178,268)(179,270)(180,269)(181,286)(182,288)(183,287)
(184,283)(185,285)(186,284)(187,280)(188,282)(189,281)(190,277)(191,279)
(192,278);
s1 := Sym(384)!( 1, 3)( 4, 6)( 7, 9)( 10, 12)( 13, 21)( 14, 20)( 15, 19)
( 16, 24)( 17, 23)( 18, 22)( 25, 27)( 28, 30)( 31, 33)( 34, 36)( 37, 45)
( 38, 44)( 39, 43)( 40, 48)( 41, 47)( 42, 46)( 49, 54)( 50, 53)( 51, 52)
( 55, 60)( 56, 59)( 57, 58)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)
( 66, 67)( 73, 78)( 74, 77)( 75, 76)( 79, 84)( 80, 83)( 81, 82)( 85, 96)
( 86, 95)( 87, 94)( 88, 93)( 89, 92)( 90, 91)( 97,123)( 98,122)( 99,121)
(100,126)(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)(107,131)
(108,130)(109,141)(110,140)(111,139)(112,144)(113,143)(114,142)(115,135)
(116,134)(117,133)(118,138)(119,137)(120,136)(145,177)(146,176)(147,175)
(148,180)(149,179)(150,178)(151,171)(152,170)(153,169)(154,174)(155,173)
(156,172)(157,183)(158,182)(159,181)(160,186)(161,185)(162,184)(163,189)
(164,188)(165,187)(166,192)(167,191)(168,190)(193,243)(194,242)(195,241)
(196,246)(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)(203,251)
(204,250)(205,261)(206,260)(207,259)(208,264)(209,263)(210,262)(211,255)
(212,254)(213,253)(214,258)(215,257)(216,256)(217,267)(218,266)(219,265)
(220,270)(221,269)(222,268)(223,273)(224,272)(225,271)(226,276)(227,275)
(228,274)(229,285)(230,284)(231,283)(232,288)(233,287)(234,286)(235,279)
(236,278)(237,277)(238,282)(239,281)(240,280)(289,378)(290,377)(291,376)
(292,375)(293,374)(294,373)(295,384)(296,383)(297,382)(298,381)(299,380)
(300,379)(301,369)(302,368)(303,367)(304,372)(305,371)(306,370)(307,363)
(308,362)(309,361)(310,366)(311,365)(312,364)(313,351)(314,350)(315,349)
(316,354)(317,353)(318,352)(319,357)(320,356)(321,355)(322,360)(323,359)
(324,358)(325,348)(326,347)(327,346)(328,345)(329,344)(330,343)(331,342)
(332,341)(333,340)(334,339)(335,338)(336,337);
s2 := Sym(384)!( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,202)
( 8,203)( 9,204)( 10,199)( 11,200)( 12,201)( 13,205)( 14,206)( 15,207)
( 16,208)( 17,209)( 18,210)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)
( 24,213)( 25,238)( 26,239)( 27,240)( 28,235)( 29,236)( 30,237)( 31,229)
( 32,230)( 33,231)( 34,232)( 35,233)( 36,234)( 37,223)( 38,224)( 39,225)
( 40,226)( 41,227)( 42,228)( 43,220)( 44,221)( 45,222)( 46,217)( 47,218)
( 48,219)( 49,244)( 50,245)( 51,246)( 52,241)( 53,242)( 54,243)( 55,247)
( 56,248)( 57,249)( 58,250)( 59,251)( 60,252)( 61,256)( 62,257)( 63,258)
( 64,253)( 65,254)( 66,255)( 67,259)( 68,260)( 69,261)( 70,262)( 71,263)
( 72,264)( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,280)
( 80,281)( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)
( 88,271)( 89,272)( 90,273)( 91,265)( 92,266)( 93,267)( 94,268)( 95,269)
( 96,270)( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)
(104,299)(105,300)(106,295)(107,296)(108,297)(109,301)(110,302)(111,303)
(112,304)(113,305)(114,306)(115,310)(116,311)(117,312)(118,307)(119,308)
(120,309)(121,334)(122,335)(123,336)(124,331)(125,332)(126,333)(127,325)
(128,326)(129,327)(130,328)(131,329)(132,330)(133,319)(134,320)(135,321)
(136,322)(137,323)(138,324)(139,316)(140,317)(141,318)(142,313)(143,314)
(144,315)(145,340)(146,341)(147,342)(148,337)(149,338)(150,339)(151,343)
(152,344)(153,345)(154,346)(155,347)(156,348)(157,352)(158,353)(159,354)
(160,349)(161,350)(162,351)(163,355)(164,356)(165,357)(166,358)(167,359)
(168,360)(169,379)(170,380)(171,381)(172,382)(173,383)(174,384)(175,376)
(176,377)(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)
(184,367)(185,368)(186,369)(187,361)(188,362)(189,363)(190,364)(191,365)
(192,366);
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*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0 >;
References : None.
to this polytope