Polytope of Type {3,8,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,8,4}*768e
if this polytope has a name.
Group : SmallGroup(768,1088555)
Rank : 4
Schlafli Type : {3,8,4}
Number of vertices, edges, etc : 6, 48, 64, 8
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 4
Special Properties :
Orientable
Flat
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 : {3,4,4}*384b
4-fold quotients : {3,4,4}*192a
8-fold quotients : {3,4,2}*96
16-fold quotients : {3,4,2}*48
32-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,103)( 6,104)( 7,101)( 8,102)
( 9,108)( 10,107)( 11,106)( 12,105)( 13,110)( 14,109)( 15,112)( 16,111)
( 17,128)( 18,127)( 19,126)( 20,125)( 21,122)( 22,121)( 23,124)( 24,123)
( 25,118)( 26,117)( 27,120)( 28,119)( 29,116)( 30,115)( 31,114)( 32,113)
( 33,161)( 34,162)( 35,163)( 36,164)( 37,167)( 38,168)( 39,165)( 40,166)
( 41,172)( 42,171)( 43,170)( 44,169)( 45,174)( 46,173)( 47,176)( 48,175)
( 49,192)( 50,191)( 51,190)( 52,189)( 53,186)( 54,185)( 55,188)( 56,187)
( 57,182)( 58,181)( 59,184)( 60,183)( 61,180)( 62,179)( 63,178)( 64,177)
( 65,129)( 66,130)( 67,131)( 68,132)( 69,135)( 70,136)( 71,133)( 72,134)
( 73,140)( 74,139)( 75,138)( 76,137)( 77,142)( 78,141)( 79,144)( 80,143)
( 81,160)( 82,159)( 83,158)( 84,157)( 85,154)( 86,153)( 87,156)( 88,155)
( 89,150)( 90,149)( 91,152)( 92,151)( 93,148)( 94,147)( 95,146)( 96,145)
(193,289)(194,290)(195,291)(196,292)(197,295)(198,296)(199,293)(200,294)
(201,300)(202,299)(203,298)(204,297)(205,302)(206,301)(207,304)(208,303)
(209,320)(210,319)(211,318)(212,317)(213,314)(214,313)(215,316)(216,315)
(217,310)(218,309)(219,312)(220,311)(221,308)(222,307)(223,306)(224,305)
(225,353)(226,354)(227,355)(228,356)(229,359)(230,360)(231,357)(232,358)
(233,364)(234,363)(235,362)(236,361)(237,366)(238,365)(239,368)(240,367)
(241,384)(242,383)(243,382)(244,381)(245,378)(246,377)(247,380)(248,379)
(249,374)(250,373)(251,376)(252,375)(253,372)(254,371)(255,370)(256,369)
(257,321)(258,322)(259,323)(260,324)(261,327)(262,328)(263,325)(264,326)
(265,332)(266,331)(267,330)(268,329)(269,334)(270,333)(271,336)(272,335)
(273,352)(274,351)(275,350)(276,349)(277,346)(278,345)(279,348)(280,347)
(281,342)(282,341)(283,344)(284,343)(285,340)(286,339)(287,338)(288,337);;
s1 := ( 1,161)( 2,162)( 3,165)( 4,166)( 5,163)( 6,164)( 7,167)( 8,168)
( 9,182)( 10,181)( 11,178)( 12,177)( 13,184)( 14,183)( 15,180)( 16,179)
( 17,172)( 18,171)( 19,176)( 20,175)( 21,170)( 22,169)( 23,174)( 24,173)
( 25,192)( 26,191)( 27,188)( 28,187)( 29,190)( 30,189)( 31,186)( 32,185)
( 33,129)( 34,130)( 35,133)( 36,134)( 37,131)( 38,132)( 39,135)( 40,136)
( 41,150)( 42,149)( 43,146)( 44,145)( 45,152)( 46,151)( 47,148)( 48,147)
( 49,140)( 50,139)( 51,144)( 52,143)( 53,138)( 54,137)( 55,142)( 56,141)
( 57,160)( 58,159)( 59,156)( 60,155)( 61,158)( 62,157)( 63,154)( 64,153)
( 65, 97)( 66, 98)( 67,101)( 68,102)( 69, 99)( 70,100)( 71,103)( 72,104)
( 73,118)( 74,117)( 75,114)( 76,113)( 77,120)( 78,119)( 79,116)( 80,115)
( 81,108)( 82,107)( 83,112)( 84,111)( 85,106)( 86,105)( 87,110)( 88,109)
( 89,128)( 90,127)( 91,124)( 92,123)( 93,126)( 94,125)( 95,122)( 96,121)
(193,353)(194,354)(195,357)(196,358)(197,355)(198,356)(199,359)(200,360)
(201,374)(202,373)(203,370)(204,369)(205,376)(206,375)(207,372)(208,371)
(209,364)(210,363)(211,368)(212,367)(213,362)(214,361)(215,366)(216,365)
(217,384)(218,383)(219,380)(220,379)(221,382)(222,381)(223,378)(224,377)
(225,321)(226,322)(227,325)(228,326)(229,323)(230,324)(231,327)(232,328)
(233,342)(234,341)(235,338)(236,337)(237,344)(238,343)(239,340)(240,339)
(241,332)(242,331)(243,336)(244,335)(245,330)(246,329)(247,334)(248,333)
(249,352)(250,351)(251,348)(252,347)(253,350)(254,349)(255,346)(256,345)
(257,289)(258,290)(259,293)(260,294)(261,291)(262,292)(263,295)(264,296)
(265,310)(266,309)(267,306)(268,305)(269,312)(270,311)(271,308)(272,307)
(273,300)(274,299)(275,304)(276,303)(277,298)(278,297)(279,302)(280,301)
(281,320)(282,319)(283,316)(284,315)(285,318)(286,317)(287,314)(288,313);;
s2 := ( 1,205)( 2,206)( 3,207)( 4,208)( 5,202)( 6,201)( 7,204)( 8,203)
( 9,197)( 10,198)( 11,199)( 12,200)( 13,194)( 14,193)( 15,196)( 16,195)
( 17,221)( 18,222)( 19,223)( 20,224)( 21,218)( 22,217)( 23,220)( 24,219)
( 25,213)( 26,214)( 27,215)( 28,216)( 29,210)( 30,209)( 31,212)( 32,211)
( 33,237)( 34,238)( 35,239)( 36,240)( 37,234)( 38,233)( 39,236)( 40,235)
( 41,229)( 42,230)( 43,231)( 44,232)( 45,226)( 46,225)( 47,228)( 48,227)
( 49,253)( 50,254)( 51,255)( 52,256)( 53,250)( 54,249)( 55,252)( 56,251)
( 57,245)( 58,246)( 59,247)( 60,248)( 61,242)( 62,241)( 63,244)( 64,243)
( 65,269)( 66,270)( 67,271)( 68,272)( 69,266)( 70,265)( 71,268)( 72,267)
( 73,261)( 74,262)( 75,263)( 76,264)( 77,258)( 78,257)( 79,260)( 80,259)
( 81,285)( 82,286)( 83,287)( 84,288)( 85,282)( 86,281)( 87,284)( 88,283)
( 89,277)( 90,278)( 91,279)( 92,280)( 93,274)( 94,273)( 95,276)( 96,275)
( 97,302)( 98,301)( 99,304)(100,303)(101,297)(102,298)(103,299)(104,300)
(105,294)(106,293)(107,296)(108,295)(109,289)(110,290)(111,291)(112,292)
(113,318)(114,317)(115,320)(116,319)(117,313)(118,314)(119,315)(120,316)
(121,310)(122,309)(123,312)(124,311)(125,305)(126,306)(127,307)(128,308)
(129,334)(130,333)(131,336)(132,335)(133,329)(134,330)(135,331)(136,332)
(137,326)(138,325)(139,328)(140,327)(141,321)(142,322)(143,323)(144,324)
(145,350)(146,349)(147,352)(148,351)(149,345)(150,346)(151,347)(152,348)
(153,342)(154,341)(155,344)(156,343)(157,337)(158,338)(159,339)(160,340)
(161,366)(162,365)(163,368)(164,367)(165,361)(166,362)(167,363)(168,364)
(169,358)(170,357)(171,360)(172,359)(173,353)(174,354)(175,355)(176,356)
(177,382)(178,381)(179,384)(180,383)(181,377)(182,378)(183,379)(184,380)
(185,374)(186,373)(187,376)(188,375)(189,369)(190,370)(191,371)(192,372);;
s3 := ( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)
( 9,108)( 10,107)( 11,106)( 12,105)( 13,112)( 14,111)( 15,110)( 16,109)
( 17,118)( 18,117)( 19,120)( 20,119)( 21,114)( 22,113)( 23,116)( 24,115)
( 25,128)( 26,127)( 27,126)( 28,125)( 29,124)( 30,123)( 31,122)( 32,121)
( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)( 40,136)
( 41,140)( 42,139)( 43,138)( 44,137)( 45,144)( 46,143)( 47,142)( 48,141)
( 49,150)( 50,149)( 51,152)( 52,151)( 53,146)( 54,145)( 55,148)( 56,147)
( 57,160)( 58,159)( 59,158)( 60,157)( 61,156)( 62,155)( 63,154)( 64,153)
( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)( 72,168)
( 73,172)( 74,171)( 75,170)( 76,169)( 77,176)( 78,175)( 79,174)( 80,173)
( 81,182)( 82,181)( 83,184)( 84,183)( 85,178)( 86,177)( 87,180)( 88,179)
( 89,192)( 90,191)( 91,190)( 92,189)( 93,188)( 94,187)( 95,186)( 96,185)
(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)(200,296)
(201,300)(202,299)(203,298)(204,297)(205,304)(206,303)(207,302)(208,301)
(209,310)(210,309)(211,312)(212,311)(213,306)(214,305)(215,308)(216,307)
(217,320)(218,319)(219,318)(220,317)(221,316)(222,315)(223,314)(224,313)
(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)(232,328)
(233,332)(234,331)(235,330)(236,329)(237,336)(238,335)(239,334)(240,333)
(241,342)(242,341)(243,344)(244,343)(245,338)(246,337)(247,340)(248,339)
(249,352)(250,351)(251,350)(252,349)(253,348)(254,347)(255,346)(256,345)
(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)(264,360)
(265,364)(266,363)(267,362)(268,361)(269,368)(270,367)(271,366)(272,365)
(273,374)(274,373)(275,376)(276,375)(277,370)(278,369)(279,372)(280,371)
(281,384)(282,383)(283,382)(284,381)(285,380)(286,379)(287,378)(288,377);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s2*s3*s1*s2*s1*s0*s2*s1*s2*s3*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,103)( 6,104)( 7,101)
( 8,102)( 9,108)( 10,107)( 11,106)( 12,105)( 13,110)( 14,109)( 15,112)
( 16,111)( 17,128)( 18,127)( 19,126)( 20,125)( 21,122)( 22,121)( 23,124)
( 24,123)( 25,118)( 26,117)( 27,120)( 28,119)( 29,116)( 30,115)( 31,114)
( 32,113)( 33,161)( 34,162)( 35,163)( 36,164)( 37,167)( 38,168)( 39,165)
( 40,166)( 41,172)( 42,171)( 43,170)( 44,169)( 45,174)( 46,173)( 47,176)
( 48,175)( 49,192)( 50,191)( 51,190)( 52,189)( 53,186)( 54,185)( 55,188)
( 56,187)( 57,182)( 58,181)( 59,184)( 60,183)( 61,180)( 62,179)( 63,178)
( 64,177)( 65,129)( 66,130)( 67,131)( 68,132)( 69,135)( 70,136)( 71,133)
( 72,134)( 73,140)( 74,139)( 75,138)( 76,137)( 77,142)( 78,141)( 79,144)
( 80,143)( 81,160)( 82,159)( 83,158)( 84,157)( 85,154)( 86,153)( 87,156)
( 88,155)( 89,150)( 90,149)( 91,152)( 92,151)( 93,148)( 94,147)( 95,146)
( 96,145)(193,289)(194,290)(195,291)(196,292)(197,295)(198,296)(199,293)
(200,294)(201,300)(202,299)(203,298)(204,297)(205,302)(206,301)(207,304)
(208,303)(209,320)(210,319)(211,318)(212,317)(213,314)(214,313)(215,316)
(216,315)(217,310)(218,309)(219,312)(220,311)(221,308)(222,307)(223,306)
(224,305)(225,353)(226,354)(227,355)(228,356)(229,359)(230,360)(231,357)
(232,358)(233,364)(234,363)(235,362)(236,361)(237,366)(238,365)(239,368)
(240,367)(241,384)(242,383)(243,382)(244,381)(245,378)(246,377)(247,380)
(248,379)(249,374)(250,373)(251,376)(252,375)(253,372)(254,371)(255,370)
(256,369)(257,321)(258,322)(259,323)(260,324)(261,327)(262,328)(263,325)
(264,326)(265,332)(266,331)(267,330)(268,329)(269,334)(270,333)(271,336)
(272,335)(273,352)(274,351)(275,350)(276,349)(277,346)(278,345)(279,348)
(280,347)(281,342)(282,341)(283,344)(284,343)(285,340)(286,339)(287,338)
(288,337);
s1 := Sym(384)!( 1,161)( 2,162)( 3,165)( 4,166)( 5,163)( 6,164)( 7,167)
( 8,168)( 9,182)( 10,181)( 11,178)( 12,177)( 13,184)( 14,183)( 15,180)
( 16,179)( 17,172)( 18,171)( 19,176)( 20,175)( 21,170)( 22,169)( 23,174)
( 24,173)( 25,192)( 26,191)( 27,188)( 28,187)( 29,190)( 30,189)( 31,186)
( 32,185)( 33,129)( 34,130)( 35,133)( 36,134)( 37,131)( 38,132)( 39,135)
( 40,136)( 41,150)( 42,149)( 43,146)( 44,145)( 45,152)( 46,151)( 47,148)
( 48,147)( 49,140)( 50,139)( 51,144)( 52,143)( 53,138)( 54,137)( 55,142)
( 56,141)( 57,160)( 58,159)( 59,156)( 60,155)( 61,158)( 62,157)( 63,154)
( 64,153)( 65, 97)( 66, 98)( 67,101)( 68,102)( 69, 99)( 70,100)( 71,103)
( 72,104)( 73,118)( 74,117)( 75,114)( 76,113)( 77,120)( 78,119)( 79,116)
( 80,115)( 81,108)( 82,107)( 83,112)( 84,111)( 85,106)( 86,105)( 87,110)
( 88,109)( 89,128)( 90,127)( 91,124)( 92,123)( 93,126)( 94,125)( 95,122)
( 96,121)(193,353)(194,354)(195,357)(196,358)(197,355)(198,356)(199,359)
(200,360)(201,374)(202,373)(203,370)(204,369)(205,376)(206,375)(207,372)
(208,371)(209,364)(210,363)(211,368)(212,367)(213,362)(214,361)(215,366)
(216,365)(217,384)(218,383)(219,380)(220,379)(221,382)(222,381)(223,378)
(224,377)(225,321)(226,322)(227,325)(228,326)(229,323)(230,324)(231,327)
(232,328)(233,342)(234,341)(235,338)(236,337)(237,344)(238,343)(239,340)
(240,339)(241,332)(242,331)(243,336)(244,335)(245,330)(246,329)(247,334)
(248,333)(249,352)(250,351)(251,348)(252,347)(253,350)(254,349)(255,346)
(256,345)(257,289)(258,290)(259,293)(260,294)(261,291)(262,292)(263,295)
(264,296)(265,310)(266,309)(267,306)(268,305)(269,312)(270,311)(271,308)
(272,307)(273,300)(274,299)(275,304)(276,303)(277,298)(278,297)(279,302)
(280,301)(281,320)(282,319)(283,316)(284,315)(285,318)(286,317)(287,314)
(288,313);
s2 := Sym(384)!( 1,205)( 2,206)( 3,207)( 4,208)( 5,202)( 6,201)( 7,204)
( 8,203)( 9,197)( 10,198)( 11,199)( 12,200)( 13,194)( 14,193)( 15,196)
( 16,195)( 17,221)( 18,222)( 19,223)( 20,224)( 21,218)( 22,217)( 23,220)
( 24,219)( 25,213)( 26,214)( 27,215)( 28,216)( 29,210)( 30,209)( 31,212)
( 32,211)( 33,237)( 34,238)( 35,239)( 36,240)( 37,234)( 38,233)( 39,236)
( 40,235)( 41,229)( 42,230)( 43,231)( 44,232)( 45,226)( 46,225)( 47,228)
( 48,227)( 49,253)( 50,254)( 51,255)( 52,256)( 53,250)( 54,249)( 55,252)
( 56,251)( 57,245)( 58,246)( 59,247)( 60,248)( 61,242)( 62,241)( 63,244)
( 64,243)( 65,269)( 66,270)( 67,271)( 68,272)( 69,266)( 70,265)( 71,268)
( 72,267)( 73,261)( 74,262)( 75,263)( 76,264)( 77,258)( 78,257)( 79,260)
( 80,259)( 81,285)( 82,286)( 83,287)( 84,288)( 85,282)( 86,281)( 87,284)
( 88,283)( 89,277)( 90,278)( 91,279)( 92,280)( 93,274)( 94,273)( 95,276)
( 96,275)( 97,302)( 98,301)( 99,304)(100,303)(101,297)(102,298)(103,299)
(104,300)(105,294)(106,293)(107,296)(108,295)(109,289)(110,290)(111,291)
(112,292)(113,318)(114,317)(115,320)(116,319)(117,313)(118,314)(119,315)
(120,316)(121,310)(122,309)(123,312)(124,311)(125,305)(126,306)(127,307)
(128,308)(129,334)(130,333)(131,336)(132,335)(133,329)(134,330)(135,331)
(136,332)(137,326)(138,325)(139,328)(140,327)(141,321)(142,322)(143,323)
(144,324)(145,350)(146,349)(147,352)(148,351)(149,345)(150,346)(151,347)
(152,348)(153,342)(154,341)(155,344)(156,343)(157,337)(158,338)(159,339)
(160,340)(161,366)(162,365)(163,368)(164,367)(165,361)(166,362)(167,363)
(168,364)(169,358)(170,357)(171,360)(172,359)(173,353)(174,354)(175,355)
(176,356)(177,382)(178,381)(179,384)(180,383)(181,377)(182,378)(183,379)
(184,380)(185,374)(186,373)(187,376)(188,375)(189,369)(190,370)(191,371)
(192,372);
s3 := Sym(384)!( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)
( 8,104)( 9,108)( 10,107)( 11,106)( 12,105)( 13,112)( 14,111)( 15,110)
( 16,109)( 17,118)( 18,117)( 19,120)( 20,119)( 21,114)( 22,113)( 23,116)
( 24,115)( 25,128)( 26,127)( 27,126)( 28,125)( 29,124)( 30,123)( 31,122)
( 32,121)( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)
( 40,136)( 41,140)( 42,139)( 43,138)( 44,137)( 45,144)( 46,143)( 47,142)
( 48,141)( 49,150)( 50,149)( 51,152)( 52,151)( 53,146)( 54,145)( 55,148)
( 56,147)( 57,160)( 58,159)( 59,158)( 60,157)( 61,156)( 62,155)( 63,154)
( 64,153)( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)
( 72,168)( 73,172)( 74,171)( 75,170)( 76,169)( 77,176)( 78,175)( 79,174)
( 80,173)( 81,182)( 82,181)( 83,184)( 84,183)( 85,178)( 86,177)( 87,180)
( 88,179)( 89,192)( 90,191)( 91,190)( 92,189)( 93,188)( 94,187)( 95,186)
( 96,185)(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)
(200,296)(201,300)(202,299)(203,298)(204,297)(205,304)(206,303)(207,302)
(208,301)(209,310)(210,309)(211,312)(212,311)(213,306)(214,305)(215,308)
(216,307)(217,320)(218,319)(219,318)(220,317)(221,316)(222,315)(223,314)
(224,313)(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)
(232,328)(233,332)(234,331)(235,330)(236,329)(237,336)(238,335)(239,334)
(240,333)(241,342)(242,341)(243,344)(244,343)(245,338)(246,337)(247,340)
(248,339)(249,352)(250,351)(251,350)(252,349)(253,348)(254,347)(255,346)
(256,345)(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)
(264,360)(265,364)(266,363)(267,362)(268,361)(269,368)(270,367)(271,366)
(272,365)(273,374)(274,373)(275,376)(276,375)(277,370)(278,369)(279,372)
(280,371)(281,384)(282,383)(283,382)(284,381)(285,380)(286,379)(287,378)
(288,377);
poly := sub<Sym(384)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s2*s3*s1*s2*s1*s0*s2*s1*s2*s3*s2*s0*s1*s2*s0*s1 >;
References : None.
to this polytope