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