Polytope of Type {8,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,24}*768b
if this polytope has a name.
Group : SmallGroup(768,81598)
Rank : 3
Schlafli Type : {8,24}
Number of vertices, edges, etc : 16, 192, 48
Order of s0s1s2 : 12
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}*384b, {8,12}*384b
3-fold quotients : {8,8}*256b
4-fold quotients : {4,12}*192a
6-fold quotients : {4,8}*128b, {8,4}*128b
8-fold quotients : {4,12}*96a
12-fold quotients : {4,4}*64
16-fold quotients : {2,12}*48, {4,6}*48a
24-fold quotients : {4,4}*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)
( 25,226)( 26,227)( 27,228)( 28,223)( 29,224)( 30,225)( 31,220)( 32,221)
( 33,222)( 34,217)( 35,218)( 36,219)( 37,238)( 38,239)( 39,240)( 40,235)
( 41,236)( 42,237)( 43,232)( 44,233)( 45,234)( 46,229)( 47,230)( 48,231)
( 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)
( 73,286)( 74,287)( 75,288)( 76,283)( 77,284)( 78,285)( 79,280)( 80,281)
( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)( 88,271)
( 89,272)( 90,273)( 91,268)( 92,269)( 93,270)( 94,265)( 95,266)( 96,267)
( 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)
(121,322)(122,323)(123,324)(124,319)(125,320)(126,321)(127,316)(128,317)
(129,318)(130,313)(131,314)(132,315)(133,334)(134,335)(135,336)(136,331)
(137,332)(138,333)(139,328)(140,329)(141,330)(142,325)(143,326)(144,327)
(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)
(169,382)(170,383)(171,384)(172,379)(173,380)(174,381)(175,376)(176,377)
(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)(184,367)
(185,368)(186,369)(187,364)(188,365)(189,366)(190,361)(191,362)(192,363);;
s1 := ( 2, 3)( 5, 6)( 7, 10)( 8, 12)( 9, 11)( 14, 15)( 17, 18)( 19, 22)
( 20, 24)( 21, 23)( 26, 27)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 38, 39)
( 41, 42)( 43, 46)( 44, 48)( 45, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 64)
( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)( 58, 67)( 59, 69)( 60, 68)
( 73, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 90)( 78, 89)( 79, 94)( 80, 96)
( 81, 95)( 82, 91)( 83, 93)( 84, 92)( 97,121)( 98,123)( 99,122)(100,124)
(101,126)(102,125)(103,130)(104,132)(105,131)(106,127)(107,129)(108,128)
(109,133)(110,135)(111,134)(112,136)(113,138)(114,137)(115,142)(116,144)
(117,143)(118,139)(119,141)(120,140)(145,184)(146,186)(147,185)(148,181)
(149,183)(150,182)(151,187)(152,189)(153,188)(154,190)(155,192)(156,191)
(157,172)(158,174)(159,173)(160,169)(161,171)(162,170)(163,175)(164,177)
(165,176)(166,178)(167,180)(168,179)(193,241)(194,243)(195,242)(196,244)
(197,246)(198,245)(199,250)(200,252)(201,251)(202,247)(203,249)(204,248)
(205,253)(206,255)(207,254)(208,256)(209,258)(210,257)(211,262)(212,264)
(213,263)(214,259)(215,261)(216,260)(217,265)(218,267)(219,266)(220,268)
(221,270)(222,269)(223,274)(224,276)(225,275)(226,271)(227,273)(228,272)
(229,277)(230,279)(231,278)(232,280)(233,282)(234,281)(235,286)(236,288)
(237,287)(238,283)(239,285)(240,284)(289,367)(290,369)(291,368)(292,370)
(293,372)(294,371)(295,364)(296,366)(297,365)(298,361)(299,363)(300,362)
(301,379)(302,381)(303,380)(304,382)(305,384)(306,383)(307,376)(308,378)
(309,377)(310,373)(311,375)(312,374)(313,343)(314,345)(315,344)(316,346)
(317,348)(318,347)(319,340)(320,342)(321,341)(322,337)(323,339)(324,338)
(325,355)(326,357)(327,356)(328,358)(329,360)(330,359)(331,352)(332,354)
(333,353)(334,349)(335,351)(336,350);;
s2 := ( 1,291)( 2,290)( 3,289)( 4,294)( 5,293)( 6,292)( 7,297)( 8,296)
( 9,295)( 10,300)( 11,299)( 12,298)( 13,303)( 14,302)( 15,301)( 16,306)
( 17,305)( 18,304)( 19,309)( 20,308)( 21,307)( 22,312)( 23,311)( 24,310)
( 25,324)( 26,323)( 27,322)( 28,321)( 29,320)( 30,319)( 31,318)( 32,317)
( 33,316)( 34,315)( 35,314)( 36,313)( 37,336)( 38,335)( 39,334)( 40,333)
( 41,332)( 42,331)( 43,330)( 44,329)( 45,328)( 46,327)( 47,326)( 48,325)
( 49,357)( 50,356)( 51,355)( 52,360)( 53,359)( 54,358)( 55,351)( 56,350)
( 57,349)( 58,354)( 59,353)( 60,352)( 61,345)( 62,344)( 63,343)( 64,348)
( 65,347)( 66,346)( 67,339)( 68,338)( 69,337)( 70,342)( 71,341)( 72,340)
( 73,378)( 74,377)( 75,376)( 76,375)( 77,374)( 78,373)( 79,384)( 80,383)
( 81,382)( 82,381)( 83,380)( 84,379)( 85,366)( 86,365)( 87,364)( 88,363)
( 89,362)( 90,361)( 91,372)( 92,371)( 93,370)( 94,369)( 95,368)( 96,367)
( 97,195)( 98,194)( 99,193)(100,198)(101,197)(102,196)(103,201)(104,200)
(105,199)(106,204)(107,203)(108,202)(109,207)(110,206)(111,205)(112,210)
(113,209)(114,208)(115,213)(116,212)(117,211)(118,216)(119,215)(120,214)
(121,228)(122,227)(123,226)(124,225)(125,224)(126,223)(127,222)(128,221)
(129,220)(130,219)(131,218)(132,217)(133,240)(134,239)(135,238)(136,237)
(137,236)(138,235)(139,234)(140,233)(141,232)(142,231)(143,230)(144,229)
(145,261)(146,260)(147,259)(148,264)(149,263)(150,262)(151,255)(152,254)
(153,253)(154,258)(155,257)(156,256)(157,249)(158,248)(159,247)(160,252)
(161,251)(162,250)(163,243)(164,242)(165,241)(166,246)(167,245)(168,244)
(169,282)(170,281)(171,280)(172,279)(173,278)(174,277)(175,288)(176,287)
(177,286)(178,285)(179,284)(180,283)(181,270)(182,269)(183,268)(184,267)
(185,266)(186,265)(187,276)(188,275)(189,274)(190,273)(191,272)(192,271);;
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,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0 ];;
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)( 25,226)( 26,227)( 27,228)( 28,223)( 29,224)( 30,225)( 31,220)
( 32,221)( 33,222)( 34,217)( 35,218)( 36,219)( 37,238)( 38,239)( 39,240)
( 40,235)( 41,236)( 42,237)( 43,232)( 44,233)( 45,234)( 46,229)( 47,230)
( 48,231)( 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)( 73,286)( 74,287)( 75,288)( 76,283)( 77,284)( 78,285)( 79,280)
( 80,281)( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)
( 88,271)( 89,272)( 90,273)( 91,268)( 92,269)( 93,270)( 94,265)( 95,266)
( 96,267)( 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)(121,322)(122,323)(123,324)(124,319)(125,320)(126,321)(127,316)
(128,317)(129,318)(130,313)(131,314)(132,315)(133,334)(134,335)(135,336)
(136,331)(137,332)(138,333)(139,328)(140,329)(141,330)(142,325)(143,326)
(144,327)(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)(169,382)(170,383)(171,384)(172,379)(173,380)(174,381)(175,376)
(176,377)(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)
(184,367)(185,368)(186,369)(187,364)(188,365)(189,366)(190,361)(191,362)
(192,363);
s1 := Sym(384)!( 2, 3)( 5, 6)( 7, 10)( 8, 12)( 9, 11)( 14, 15)( 17, 18)
( 19, 22)( 20, 24)( 21, 23)( 26, 27)( 29, 30)( 31, 34)( 32, 36)( 33, 35)
( 38, 39)( 41, 42)( 43, 46)( 44, 48)( 45, 47)( 49, 61)( 50, 63)( 51, 62)
( 52, 64)( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)( 58, 67)( 59, 69)
( 60, 68)( 73, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 90)( 78, 89)( 79, 94)
( 80, 96)( 81, 95)( 82, 91)( 83, 93)( 84, 92)( 97,121)( 98,123)( 99,122)
(100,124)(101,126)(102,125)(103,130)(104,132)(105,131)(106,127)(107,129)
(108,128)(109,133)(110,135)(111,134)(112,136)(113,138)(114,137)(115,142)
(116,144)(117,143)(118,139)(119,141)(120,140)(145,184)(146,186)(147,185)
(148,181)(149,183)(150,182)(151,187)(152,189)(153,188)(154,190)(155,192)
(156,191)(157,172)(158,174)(159,173)(160,169)(161,171)(162,170)(163,175)
(164,177)(165,176)(166,178)(167,180)(168,179)(193,241)(194,243)(195,242)
(196,244)(197,246)(198,245)(199,250)(200,252)(201,251)(202,247)(203,249)
(204,248)(205,253)(206,255)(207,254)(208,256)(209,258)(210,257)(211,262)
(212,264)(213,263)(214,259)(215,261)(216,260)(217,265)(218,267)(219,266)
(220,268)(221,270)(222,269)(223,274)(224,276)(225,275)(226,271)(227,273)
(228,272)(229,277)(230,279)(231,278)(232,280)(233,282)(234,281)(235,286)
(236,288)(237,287)(238,283)(239,285)(240,284)(289,367)(290,369)(291,368)
(292,370)(293,372)(294,371)(295,364)(296,366)(297,365)(298,361)(299,363)
(300,362)(301,379)(302,381)(303,380)(304,382)(305,384)(306,383)(307,376)
(308,378)(309,377)(310,373)(311,375)(312,374)(313,343)(314,345)(315,344)
(316,346)(317,348)(318,347)(319,340)(320,342)(321,341)(322,337)(323,339)
(324,338)(325,355)(326,357)(327,356)(328,358)(329,360)(330,359)(331,352)
(332,354)(333,353)(334,349)(335,351)(336,350);
s2 := Sym(384)!( 1,291)( 2,290)( 3,289)( 4,294)( 5,293)( 6,292)( 7,297)
( 8,296)( 9,295)( 10,300)( 11,299)( 12,298)( 13,303)( 14,302)( 15,301)
( 16,306)( 17,305)( 18,304)( 19,309)( 20,308)( 21,307)( 22,312)( 23,311)
( 24,310)( 25,324)( 26,323)( 27,322)( 28,321)( 29,320)( 30,319)( 31,318)
( 32,317)( 33,316)( 34,315)( 35,314)( 36,313)( 37,336)( 38,335)( 39,334)
( 40,333)( 41,332)( 42,331)( 43,330)( 44,329)( 45,328)( 46,327)( 47,326)
( 48,325)( 49,357)( 50,356)( 51,355)( 52,360)( 53,359)( 54,358)( 55,351)
( 56,350)( 57,349)( 58,354)( 59,353)( 60,352)( 61,345)( 62,344)( 63,343)
( 64,348)( 65,347)( 66,346)( 67,339)( 68,338)( 69,337)( 70,342)( 71,341)
( 72,340)( 73,378)( 74,377)( 75,376)( 76,375)( 77,374)( 78,373)( 79,384)
( 80,383)( 81,382)( 82,381)( 83,380)( 84,379)( 85,366)( 86,365)( 87,364)
( 88,363)( 89,362)( 90,361)( 91,372)( 92,371)( 93,370)( 94,369)( 95,368)
( 96,367)( 97,195)( 98,194)( 99,193)(100,198)(101,197)(102,196)(103,201)
(104,200)(105,199)(106,204)(107,203)(108,202)(109,207)(110,206)(111,205)
(112,210)(113,209)(114,208)(115,213)(116,212)(117,211)(118,216)(119,215)
(120,214)(121,228)(122,227)(123,226)(124,225)(125,224)(126,223)(127,222)
(128,221)(129,220)(130,219)(131,218)(132,217)(133,240)(134,239)(135,238)
(136,237)(137,236)(138,235)(139,234)(140,233)(141,232)(142,231)(143,230)
(144,229)(145,261)(146,260)(147,259)(148,264)(149,263)(150,262)(151,255)
(152,254)(153,253)(154,258)(155,257)(156,256)(157,249)(158,248)(159,247)
(160,252)(161,251)(162,250)(163,243)(164,242)(165,241)(166,246)(167,245)
(168,244)(169,282)(170,281)(171,280)(172,279)(173,278)(174,277)(175,288)
(176,287)(177,286)(178,285)(179,284)(180,283)(181,270)(182,269)(183,268)
(184,267)(185,266)(186,265)(187,276)(188,275)(189,274)(190,273)(191,272)
(192,271);
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,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0 >;
References : None.
to this polytope