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