Polytope of Type {24,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*768p
if this polytope has a name.
Group : SmallGroup(768,1086909)
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
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,8}*384h, {24,4}*384f
4-fold quotients : {12,4}*192c, {6,8}*192b
8-fold quotients : {3,8}*96, {6,4}*96
16-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
32-fold quotients : {3,4}*24, {6,2}*24
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 := ( 1,194)( 2,193)( 3,195)( 4,196)( 5,200)( 6,199)( 7,198)( 8,197)
( 9,210)( 10,209)( 11,211)( 12,212)( 13,216)( 14,215)( 15,214)( 16,213)
( 17,202)( 18,201)( 19,203)( 20,204)( 21,208)( 22,207)( 23,206)( 24,205)
( 25,218)( 26,217)( 27,219)( 28,220)( 29,224)( 30,223)( 31,222)( 32,221)
( 33,234)( 34,233)( 35,235)( 36,236)( 37,240)( 38,239)( 39,238)( 40,237)
( 41,226)( 42,225)( 43,227)( 44,228)( 45,232)( 46,231)( 47,230)( 48,229)
( 49,266)( 50,265)( 51,267)( 52,268)( 53,272)( 54,271)( 55,270)( 56,269)
( 57,282)( 58,281)( 59,283)( 60,284)( 61,288)( 62,287)( 63,286)( 64,285)
( 65,274)( 66,273)( 67,275)( 68,276)( 69,280)( 70,279)( 71,278)( 72,277)
( 73,242)( 74,241)( 75,243)( 76,244)( 77,248)( 78,247)( 79,246)( 80,245)
( 81,258)( 82,257)( 83,259)( 84,260)( 85,264)( 86,263)( 87,262)( 88,261)
( 89,250)( 90,249)( 91,251)( 92,252)( 93,256)( 94,255)( 95,254)( 96,253)
( 97,361)( 98,362)( 99,364)(100,363)(101,367)(102,368)(103,365)(104,366)
(105,377)(106,378)(107,380)(108,379)(109,383)(110,384)(111,381)(112,382)
(113,369)(114,370)(115,372)(116,371)(117,375)(118,376)(119,373)(120,374)
(121,337)(122,338)(123,340)(124,339)(125,343)(126,344)(127,341)(128,342)
(129,353)(130,354)(131,356)(132,355)(133,359)(134,360)(135,357)(136,358)
(137,345)(138,346)(139,348)(140,347)(141,351)(142,352)(143,349)(144,350)
(145,313)(146,314)(147,316)(148,315)(149,319)(150,320)(151,317)(152,318)
(153,329)(154,330)(155,332)(156,331)(157,335)(158,336)(159,333)(160,334)
(161,321)(162,322)(163,324)(164,323)(165,327)(166,328)(167,325)(168,326)
(169,289)(170,290)(171,292)(172,291)(173,295)(174,296)(175,293)(176,294)
(177,305)(178,306)(179,308)(180,307)(181,311)(182,312)(183,309)(184,310)
(185,297)(186,298)(187,300)(188,299)(189,303)(190,304)(191,301)(192,302);;
s1 := ( 1,138)( 2,137)( 3,141)( 4,142)( 5,139)( 6,140)( 7,143)( 8,144)
( 9,130)( 10,129)( 11,133)( 12,134)( 13,131)( 14,132)( 15,135)( 16,136)
( 17,122)( 18,121)( 19,125)( 20,126)( 21,123)( 22,124)( 23,127)( 24,128)
( 25,114)( 26,113)( 27,117)( 28,118)( 29,115)( 30,116)( 31,119)( 32,120)
( 33,106)( 34,105)( 35,109)( 36,110)( 37,107)( 38,108)( 39,111)( 40,112)
( 41, 98)( 42, 97)( 43,101)( 44,102)( 45, 99)( 46,100)( 47,103)( 48,104)
( 49,162)( 50,161)( 51,165)( 52,166)( 53,163)( 54,164)( 55,167)( 56,168)
( 57,154)( 58,153)( 59,157)( 60,158)( 61,155)( 62,156)( 63,159)( 64,160)
( 65,146)( 66,145)( 67,149)( 68,150)( 69,147)( 70,148)( 71,151)( 72,152)
( 73,186)( 74,185)( 75,189)( 76,190)( 77,187)( 78,188)( 79,191)( 80,192)
( 81,178)( 82,177)( 83,181)( 84,182)( 85,179)( 86,180)( 87,183)( 88,184)
( 89,170)( 90,169)( 91,173)( 92,174)( 93,171)( 94,172)( 95,175)( 96,176)
(193,329)(194,330)(195,334)(196,333)(197,332)(198,331)(199,336)(200,335)
(201,321)(202,322)(203,326)(204,325)(205,324)(206,323)(207,328)(208,327)
(209,313)(210,314)(211,318)(212,317)(213,316)(214,315)(215,320)(216,319)
(217,305)(218,306)(219,310)(220,309)(221,308)(222,307)(223,312)(224,311)
(225,297)(226,298)(227,302)(228,301)(229,300)(230,299)(231,304)(232,303)
(233,289)(234,290)(235,294)(236,293)(237,292)(238,291)(239,296)(240,295)
(241,353)(242,354)(243,358)(244,357)(245,356)(246,355)(247,360)(248,359)
(249,345)(250,346)(251,350)(252,349)(253,348)(254,347)(255,352)(256,351)
(257,337)(258,338)(259,342)(260,341)(261,340)(262,339)(263,344)(264,343)
(265,377)(266,378)(267,382)(268,381)(269,380)(270,379)(271,384)(272,383)
(273,369)(274,370)(275,374)(276,373)(277,372)(278,371)(279,376)(280,375)
(281,361)(282,362)(283,366)(284,365)(285,364)(286,363)(287,368)(288,367);;
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)
( 49,268)( 50,267)( 51,265)( 52,266)( 53,272)( 54,271)( 55,269)( 56,270)
( 57,276)( 58,275)( 59,273)( 60,274)( 61,280)( 62,279)( 63,277)( 64,278)
( 65,284)( 66,283)( 67,281)( 68,282)( 69,288)( 70,287)( 71,285)( 72,286)
( 73,244)( 74,243)( 75,241)( 76,242)( 77,248)( 78,247)( 79,245)( 80,246)
( 81,252)( 82,251)( 83,249)( 84,250)( 85,256)( 86,255)( 87,253)( 88,254)
( 89,260)( 90,259)( 91,257)( 92,258)( 93,264)( 94,263)( 95,261)( 96,262)
( 97,340)( 98,339)( 99,337)(100,338)(101,344)(102,343)(103,341)(104,342)
(105,348)(106,347)(107,345)(108,346)(109,352)(110,351)(111,349)(112,350)
(113,356)(114,355)(115,353)(116,354)(117,360)(118,359)(119,357)(120,358)
(121,364)(122,363)(123,361)(124,362)(125,368)(126,367)(127,365)(128,366)
(129,372)(130,371)(131,369)(132,370)(133,376)(134,375)(135,373)(136,374)
(137,380)(138,379)(139,377)(140,378)(141,384)(142,383)(143,381)(144,382)
(145,292)(146,291)(147,289)(148,290)(149,296)(150,295)(151,293)(152,294)
(153,300)(154,299)(155,297)(156,298)(157,304)(158,303)(159,301)(160,302)
(161,308)(162,307)(163,305)(164,306)(165,312)(166,311)(167,309)(168,310)
(169,316)(170,315)(171,313)(172,314)(173,320)(174,319)(175,317)(176,318)
(177,324)(178,323)(179,321)(180,322)(181,328)(182,327)(183,325)(184,326)
(185,332)(186,331)(187,329)(188,330)(189,336)(190,335)(191,333)(192,334);;
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,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1,194)( 2,193)( 3,195)( 4,196)( 5,200)( 6,199)( 7,198)
( 8,197)( 9,210)( 10,209)( 11,211)( 12,212)( 13,216)( 14,215)( 15,214)
( 16,213)( 17,202)( 18,201)( 19,203)( 20,204)( 21,208)( 22,207)( 23,206)
( 24,205)( 25,218)( 26,217)( 27,219)( 28,220)( 29,224)( 30,223)( 31,222)
( 32,221)( 33,234)( 34,233)( 35,235)( 36,236)( 37,240)( 38,239)( 39,238)
( 40,237)( 41,226)( 42,225)( 43,227)( 44,228)( 45,232)( 46,231)( 47,230)
( 48,229)( 49,266)( 50,265)( 51,267)( 52,268)( 53,272)( 54,271)( 55,270)
( 56,269)( 57,282)( 58,281)( 59,283)( 60,284)( 61,288)( 62,287)( 63,286)
( 64,285)( 65,274)( 66,273)( 67,275)( 68,276)( 69,280)( 70,279)( 71,278)
( 72,277)( 73,242)( 74,241)( 75,243)( 76,244)( 77,248)( 78,247)( 79,246)
( 80,245)( 81,258)( 82,257)( 83,259)( 84,260)( 85,264)( 86,263)( 87,262)
( 88,261)( 89,250)( 90,249)( 91,251)( 92,252)( 93,256)( 94,255)( 95,254)
( 96,253)( 97,361)( 98,362)( 99,364)(100,363)(101,367)(102,368)(103,365)
(104,366)(105,377)(106,378)(107,380)(108,379)(109,383)(110,384)(111,381)
(112,382)(113,369)(114,370)(115,372)(116,371)(117,375)(118,376)(119,373)
(120,374)(121,337)(122,338)(123,340)(124,339)(125,343)(126,344)(127,341)
(128,342)(129,353)(130,354)(131,356)(132,355)(133,359)(134,360)(135,357)
(136,358)(137,345)(138,346)(139,348)(140,347)(141,351)(142,352)(143,349)
(144,350)(145,313)(146,314)(147,316)(148,315)(149,319)(150,320)(151,317)
(152,318)(153,329)(154,330)(155,332)(156,331)(157,335)(158,336)(159,333)
(160,334)(161,321)(162,322)(163,324)(164,323)(165,327)(166,328)(167,325)
(168,326)(169,289)(170,290)(171,292)(172,291)(173,295)(174,296)(175,293)
(176,294)(177,305)(178,306)(179,308)(180,307)(181,311)(182,312)(183,309)
(184,310)(185,297)(186,298)(187,300)(188,299)(189,303)(190,304)(191,301)
(192,302);
s1 := Sym(384)!( 1,138)( 2,137)( 3,141)( 4,142)( 5,139)( 6,140)( 7,143)
( 8,144)( 9,130)( 10,129)( 11,133)( 12,134)( 13,131)( 14,132)( 15,135)
( 16,136)( 17,122)( 18,121)( 19,125)( 20,126)( 21,123)( 22,124)( 23,127)
( 24,128)( 25,114)( 26,113)( 27,117)( 28,118)( 29,115)( 30,116)( 31,119)
( 32,120)( 33,106)( 34,105)( 35,109)( 36,110)( 37,107)( 38,108)( 39,111)
( 40,112)( 41, 98)( 42, 97)( 43,101)( 44,102)( 45, 99)( 46,100)( 47,103)
( 48,104)( 49,162)( 50,161)( 51,165)( 52,166)( 53,163)( 54,164)( 55,167)
( 56,168)( 57,154)( 58,153)( 59,157)( 60,158)( 61,155)( 62,156)( 63,159)
( 64,160)( 65,146)( 66,145)( 67,149)( 68,150)( 69,147)( 70,148)( 71,151)
( 72,152)( 73,186)( 74,185)( 75,189)( 76,190)( 77,187)( 78,188)( 79,191)
( 80,192)( 81,178)( 82,177)( 83,181)( 84,182)( 85,179)( 86,180)( 87,183)
( 88,184)( 89,170)( 90,169)( 91,173)( 92,174)( 93,171)( 94,172)( 95,175)
( 96,176)(193,329)(194,330)(195,334)(196,333)(197,332)(198,331)(199,336)
(200,335)(201,321)(202,322)(203,326)(204,325)(205,324)(206,323)(207,328)
(208,327)(209,313)(210,314)(211,318)(212,317)(213,316)(214,315)(215,320)
(216,319)(217,305)(218,306)(219,310)(220,309)(221,308)(222,307)(223,312)
(224,311)(225,297)(226,298)(227,302)(228,301)(229,300)(230,299)(231,304)
(232,303)(233,289)(234,290)(235,294)(236,293)(237,292)(238,291)(239,296)
(240,295)(241,353)(242,354)(243,358)(244,357)(245,356)(246,355)(247,360)
(248,359)(249,345)(250,346)(251,350)(252,349)(253,348)(254,347)(255,352)
(256,351)(257,337)(258,338)(259,342)(260,341)(261,340)(262,339)(263,344)
(264,343)(265,377)(266,378)(267,382)(268,381)(269,380)(270,379)(271,384)
(272,383)(273,369)(274,370)(275,374)(276,373)(277,372)(278,371)(279,376)
(280,375)(281,361)(282,362)(283,366)(284,365)(285,364)(286,363)(287,368)
(288,367);
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)( 49,268)( 50,267)( 51,265)( 52,266)( 53,272)( 54,271)( 55,269)
( 56,270)( 57,276)( 58,275)( 59,273)( 60,274)( 61,280)( 62,279)( 63,277)
( 64,278)( 65,284)( 66,283)( 67,281)( 68,282)( 69,288)( 70,287)( 71,285)
( 72,286)( 73,244)( 74,243)( 75,241)( 76,242)( 77,248)( 78,247)( 79,245)
( 80,246)( 81,252)( 82,251)( 83,249)( 84,250)( 85,256)( 86,255)( 87,253)
( 88,254)( 89,260)( 90,259)( 91,257)( 92,258)( 93,264)( 94,263)( 95,261)
( 96,262)( 97,340)( 98,339)( 99,337)(100,338)(101,344)(102,343)(103,341)
(104,342)(105,348)(106,347)(107,345)(108,346)(109,352)(110,351)(111,349)
(112,350)(113,356)(114,355)(115,353)(116,354)(117,360)(118,359)(119,357)
(120,358)(121,364)(122,363)(123,361)(124,362)(125,368)(126,367)(127,365)
(128,366)(129,372)(130,371)(131,369)(132,370)(133,376)(134,375)(135,373)
(136,374)(137,380)(138,379)(139,377)(140,378)(141,384)(142,383)(143,381)
(144,382)(145,292)(146,291)(147,289)(148,290)(149,296)(150,295)(151,293)
(152,294)(153,300)(154,299)(155,297)(156,298)(157,304)(158,303)(159,301)
(160,302)(161,308)(162,307)(163,305)(164,306)(165,312)(166,311)(167,309)
(168,310)(169,316)(170,315)(171,313)(172,314)(173,320)(174,319)(175,317)
(176,318)(177,324)(178,323)(179,321)(180,322)(181,328)(182,327)(183,325)
(184,326)(185,332)(186,331)(187,329)(188,330)(189,336)(190,335)(191,333)
(192,334);
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,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2 >;
References : None.
to this polytope