Polytope of Type {24,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*768b
if this polytope has a name.
Group : SmallGroup(768,81598)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 48, 192, 16
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
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, {12,8}*384b
3-fold quotients : {8,8}*256b
4-fold quotients : {12,4}*192a
6-fold quotients : {4,8}*128b, {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)( 13,301)( 14,303)( 15,302)( 16,304)
( 17,306)( 18,305)( 19,307)( 20,309)( 21,308)( 22,310)( 23,312)( 24,311)
( 25,322)( 26,324)( 27,323)( 28,319)( 29,321)( 30,320)( 31,316)( 32,318)
( 33,317)( 34,313)( 35,315)( 36,314)( 37,334)( 38,336)( 39,335)( 40,331)
( 41,333)( 42,332)( 43,328)( 44,330)( 45,329)( 46,325)( 47,327)( 48,326)
( 49,355)( 50,357)( 51,356)( 52,358)( 53,360)( 54,359)( 55,349)( 56,351)
( 57,350)( 58,352)( 59,354)( 60,353)( 61,343)( 62,345)( 63,344)( 64,346)
( 65,348)( 66,347)( 67,337)( 68,339)( 69,338)( 70,340)( 71,342)( 72,341)
( 73,376)( 74,378)( 75,377)( 76,373)( 77,375)( 78,374)( 79,382)( 80,384)
( 81,383)( 82,379)( 83,381)( 84,380)( 85,364)( 86,366)( 87,365)( 88,361)
( 89,363)( 90,362)( 91,370)( 92,372)( 93,371)( 94,367)( 95,369)( 96,368)
( 97,193)( 98,195)( 99,194)(100,196)(101,198)(102,197)(103,199)(104,201)
(105,200)(106,202)(107,204)(108,203)(109,205)(110,207)(111,206)(112,208)
(113,210)(114,209)(115,211)(116,213)(117,212)(118,214)(119,216)(120,215)
(121,226)(122,228)(123,227)(124,223)(125,225)(126,224)(127,220)(128,222)
(129,221)(130,217)(131,219)(132,218)(133,238)(134,240)(135,239)(136,235)
(137,237)(138,236)(139,232)(140,234)(141,233)(142,229)(143,231)(144,230)
(145,259)(146,261)(147,260)(148,262)(149,264)(150,263)(151,253)(152,255)
(153,254)(154,256)(155,258)(156,257)(157,247)(158,249)(159,248)(160,250)
(161,252)(162,251)(163,241)(164,243)(165,242)(166,244)(167,246)(168,245)
(169,280)(170,282)(171,281)(172,277)(173,279)(174,278)(175,286)(176,288)
(177,287)(178,283)(179,285)(180,284)(181,268)(182,270)(183,269)(184,265)
(185,267)(186,266)(187,274)(188,276)(189,275)(190,271)(191,273)(192,272);;
s1 := ( 1, 3)( 4, 6)( 7, 12)( 8, 11)( 9, 10)( 13, 15)( 16, 18)( 19, 24)
( 20, 23)( 21, 22)( 25, 27)( 28, 30)( 31, 36)( 32, 35)( 33, 34)( 37, 39)
( 40, 42)( 43, 48)( 44, 47)( 45, 46)( 49, 63)( 50, 62)( 51, 61)( 52, 66)
( 53, 65)( 54, 64)( 55, 72)( 56, 71)( 57, 70)( 58, 69)( 59, 68)( 60, 67)
( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)( 78, 88)( 79, 96)( 80, 95)
( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 97,123)( 98,122)( 99,121)(100,126)
(101,125)(102,124)(103,132)(104,131)(105,130)(106,129)(107,128)(108,127)
(109,135)(110,134)(111,133)(112,138)(113,137)(114,136)(115,144)(116,143)
(117,142)(118,141)(119,140)(120,139)(145,186)(146,185)(147,184)(148,183)
(149,182)(150,181)(151,189)(152,188)(153,187)(154,192)(155,191)(156,190)
(157,174)(158,173)(159,172)(160,171)(161,170)(162,169)(163,177)(164,176)
(165,175)(166,180)(167,179)(168,178)(193,243)(194,242)(195,241)(196,246)
(197,245)(198,244)(199,252)(200,251)(201,250)(202,249)(203,248)(204,247)
(205,255)(206,254)(207,253)(208,258)(209,257)(210,256)(211,264)(212,263)
(213,262)(214,261)(215,260)(216,259)(217,267)(218,266)(219,265)(220,270)
(221,269)(222,268)(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)
(229,279)(230,278)(231,277)(232,282)(233,281)(234,280)(235,288)(236,287)
(237,286)(238,285)(239,284)(240,283)(289,369)(290,368)(291,367)(292,372)
(293,371)(294,370)(295,366)(296,365)(297,364)(298,363)(299,362)(300,361)
(301,381)(302,380)(303,379)(304,384)(305,383)(306,382)(307,378)(308,377)
(309,376)(310,375)(311,374)(312,373)(313,345)(314,344)(315,343)(316,348)
(317,347)(318,346)(319,342)(320,341)(321,340)(322,339)(323,338)(324,337)
(325,357)(326,356)(327,355)(328,360)(329,359)(330,358)(331,354)(332,353)
(333,352)(334,351)(335,350)(336,349);;
s2 := ( 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);;
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*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1 ];;
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)( 13,301)( 14,303)( 15,302)
( 16,304)( 17,306)( 18,305)( 19,307)( 20,309)( 21,308)( 22,310)( 23,312)
( 24,311)( 25,322)( 26,324)( 27,323)( 28,319)( 29,321)( 30,320)( 31,316)
( 32,318)( 33,317)( 34,313)( 35,315)( 36,314)( 37,334)( 38,336)( 39,335)
( 40,331)( 41,333)( 42,332)( 43,328)( 44,330)( 45,329)( 46,325)( 47,327)
( 48,326)( 49,355)( 50,357)( 51,356)( 52,358)( 53,360)( 54,359)( 55,349)
( 56,351)( 57,350)( 58,352)( 59,354)( 60,353)( 61,343)( 62,345)( 63,344)
( 64,346)( 65,348)( 66,347)( 67,337)( 68,339)( 69,338)( 70,340)( 71,342)
( 72,341)( 73,376)( 74,378)( 75,377)( 76,373)( 77,375)( 78,374)( 79,382)
( 80,384)( 81,383)( 82,379)( 83,381)( 84,380)( 85,364)( 86,366)( 87,365)
( 88,361)( 89,363)( 90,362)( 91,370)( 92,372)( 93,371)( 94,367)( 95,369)
( 96,368)( 97,193)( 98,195)( 99,194)(100,196)(101,198)(102,197)(103,199)
(104,201)(105,200)(106,202)(107,204)(108,203)(109,205)(110,207)(111,206)
(112,208)(113,210)(114,209)(115,211)(116,213)(117,212)(118,214)(119,216)
(120,215)(121,226)(122,228)(123,227)(124,223)(125,225)(126,224)(127,220)
(128,222)(129,221)(130,217)(131,219)(132,218)(133,238)(134,240)(135,239)
(136,235)(137,237)(138,236)(139,232)(140,234)(141,233)(142,229)(143,231)
(144,230)(145,259)(146,261)(147,260)(148,262)(149,264)(150,263)(151,253)
(152,255)(153,254)(154,256)(155,258)(156,257)(157,247)(158,249)(159,248)
(160,250)(161,252)(162,251)(163,241)(164,243)(165,242)(166,244)(167,246)
(168,245)(169,280)(170,282)(171,281)(172,277)(173,279)(174,278)(175,286)
(176,288)(177,287)(178,283)(179,285)(180,284)(181,268)(182,270)(183,269)
(184,265)(185,267)(186,266)(187,274)(188,276)(189,275)(190,271)(191,273)
(192,272);
s1 := Sym(384)!( 1, 3)( 4, 6)( 7, 12)( 8, 11)( 9, 10)( 13, 15)( 16, 18)
( 19, 24)( 20, 23)( 21, 22)( 25, 27)( 28, 30)( 31, 36)( 32, 35)( 33, 34)
( 37, 39)( 40, 42)( 43, 48)( 44, 47)( 45, 46)( 49, 63)( 50, 62)( 51, 61)
( 52, 66)( 53, 65)( 54, 64)( 55, 72)( 56, 71)( 57, 70)( 58, 69)( 59, 68)
( 60, 67)( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)( 78, 88)( 79, 96)
( 80, 95)( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 97,123)( 98,122)( 99,121)
(100,126)(101,125)(102,124)(103,132)(104,131)(105,130)(106,129)(107,128)
(108,127)(109,135)(110,134)(111,133)(112,138)(113,137)(114,136)(115,144)
(116,143)(117,142)(118,141)(119,140)(120,139)(145,186)(146,185)(147,184)
(148,183)(149,182)(150,181)(151,189)(152,188)(153,187)(154,192)(155,191)
(156,190)(157,174)(158,173)(159,172)(160,171)(161,170)(162,169)(163,177)
(164,176)(165,175)(166,180)(167,179)(168,178)(193,243)(194,242)(195,241)
(196,246)(197,245)(198,244)(199,252)(200,251)(201,250)(202,249)(203,248)
(204,247)(205,255)(206,254)(207,253)(208,258)(209,257)(210,256)(211,264)
(212,263)(213,262)(214,261)(215,260)(216,259)(217,267)(218,266)(219,265)
(220,270)(221,269)(222,268)(223,276)(224,275)(225,274)(226,273)(227,272)
(228,271)(229,279)(230,278)(231,277)(232,282)(233,281)(234,280)(235,288)
(236,287)(237,286)(238,285)(239,284)(240,283)(289,369)(290,368)(291,367)
(292,372)(293,371)(294,370)(295,366)(296,365)(297,364)(298,363)(299,362)
(300,361)(301,381)(302,380)(303,379)(304,384)(305,383)(306,382)(307,378)
(308,377)(309,376)(310,375)(311,374)(312,373)(313,345)(314,344)(315,343)
(316,348)(317,347)(318,346)(319,342)(320,341)(321,340)(322,339)(323,338)
(324,337)(325,357)(326,356)(327,355)(328,360)(329,359)(330,358)(331,354)
(332,353)(333,352)(334,351)(335,350)(336,349);
s2 := 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);
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*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1 >;
References : None.
to this polytope