Polytope of Type {4,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,4}*768f
if this polytope has a name.
Group : SmallGroup(768,1088705)
Rank : 4
Schlafli Type : {4,12,4}
Number of vertices, edges, etc : 8, 48, 48, 4
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {4,12,4}*384d, {4,12,4}*384e, {4,12,2}*384b, {4,6,4}*384b
4-fold quotients : {2,12,4}*192a, {4,12,2}*192b, {4,12,2}*192c, {4,6,4}*192c, {4,6,2}*192
8-fold quotients : {2,12,2}*96, {2,6,4}*96a, {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
12-fold quotients : {2,4,4}*64
16-fold quotients : {4,3,2}*48, {2,6,2}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*32
32-fold quotients : {2,3,2}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,196)( 2,195)( 3,194)( 4,193)( 5,200)( 6,199)( 7,198)( 8,197)
( 9,204)( 10,203)( 11,202)( 12,201)( 13,208)( 14,207)( 15,206)( 16,205)
( 17,212)( 18,211)( 19,210)( 20,209)( 21,216)( 22,215)( 23,214)( 24,213)
( 25,220)( 26,219)( 27,218)( 28,217)( 29,224)( 30,223)( 31,222)( 32,221)
( 33,228)( 34,227)( 35,226)( 36,225)( 37,232)( 38,231)( 39,230)( 40,229)
( 41,236)( 42,235)( 43,234)( 44,233)( 45,240)( 46,239)( 47,238)( 48,237)
( 49,244)( 50,243)( 51,242)( 52,241)( 53,248)( 54,247)( 55,246)( 56,245)
( 57,252)( 58,251)( 59,250)( 60,249)( 61,256)( 62,255)( 63,254)( 64,253)
( 65,260)( 66,259)( 67,258)( 68,257)( 69,264)( 70,263)( 71,262)( 72,261)
( 73,268)( 74,267)( 75,266)( 76,265)( 77,272)( 78,271)( 79,270)( 80,269)
( 81,276)( 82,275)( 83,274)( 84,273)( 85,280)( 86,279)( 87,278)( 88,277)
( 89,284)( 90,283)( 91,282)( 92,281)( 93,288)( 94,287)( 95,286)( 96,285)
( 97,292)( 98,291)( 99,290)(100,289)(101,296)(102,295)(103,294)(104,293)
(105,300)(106,299)(107,298)(108,297)(109,304)(110,303)(111,302)(112,301)
(113,308)(114,307)(115,306)(116,305)(117,312)(118,311)(119,310)(120,309)
(121,316)(122,315)(123,314)(124,313)(125,320)(126,319)(127,318)(128,317)
(129,324)(130,323)(131,322)(132,321)(133,328)(134,327)(135,326)(136,325)
(137,332)(138,331)(139,330)(140,329)(141,336)(142,335)(143,334)(144,333)
(145,340)(146,339)(147,338)(148,337)(149,344)(150,343)(151,342)(152,341)
(153,348)(154,347)(155,346)(156,345)(157,352)(158,351)(159,350)(160,349)
(161,356)(162,355)(163,354)(164,353)(165,360)(166,359)(167,358)(168,357)
(169,364)(170,363)(171,362)(172,361)(173,368)(174,367)(175,366)(176,365)
(177,372)(178,371)(179,370)(180,369)(181,376)(182,375)(183,374)(184,373)
(185,380)(186,379)(187,378)(188,377)(189,384)(190,383)(191,382)(192,381);;
s1 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)( 18, 22)
( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 39, 40)
( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 61)( 50, 62)( 51, 64)( 52, 63)
( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 65)( 58, 66)( 59, 68)( 60, 67)
( 73, 85)( 74, 86)( 75, 88)( 76, 87)( 77, 93)( 78, 94)( 79, 96)( 80, 95)
( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 99,100)(101,105)(102,106)(103,108)
(104,107)(111,112)(113,117)(114,118)(115,120)(116,119)(123,124)(125,129)
(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)(139,144)(140,143)
(145,157)(146,158)(147,160)(148,159)(149,165)(150,166)(151,168)(152,167)
(153,161)(154,162)(155,164)(156,163)(169,181)(170,182)(171,184)(172,183)
(173,189)(174,190)(175,192)(176,191)(177,185)(178,186)(179,188)(180,187)
(195,196)(197,201)(198,202)(199,204)(200,203)(207,208)(209,213)(210,214)
(211,216)(212,215)(219,220)(221,225)(222,226)(223,228)(224,227)(231,232)
(233,237)(234,238)(235,240)(236,239)(241,253)(242,254)(243,256)(244,255)
(245,261)(246,262)(247,264)(248,263)(249,257)(250,258)(251,260)(252,259)
(265,277)(266,278)(267,280)(268,279)(269,285)(270,286)(271,288)(272,287)
(273,281)(274,282)(275,284)(276,283)(291,292)(293,297)(294,298)(295,300)
(296,299)(303,304)(305,309)(306,310)(307,312)(308,311)(315,316)(317,321)
(318,322)(319,324)(320,323)(327,328)(329,333)(330,334)(331,336)(332,335)
(337,349)(338,350)(339,352)(340,351)(341,357)(342,358)(343,360)(344,359)
(345,353)(346,354)(347,356)(348,355)(361,373)(362,374)(363,376)(364,375)
(365,381)(366,382)(367,384)(368,383)(369,377)(370,378)(371,380)(372,379);;
s2 := ( 1, 69)( 2, 71)( 3, 70)( 4, 72)( 5, 65)( 6, 67)( 7, 66)( 8, 68)
( 9, 61)( 10, 63)( 11, 62)( 12, 64)( 13, 57)( 14, 59)( 15, 58)( 16, 60)
( 17, 53)( 18, 55)( 19, 54)( 20, 56)( 21, 49)( 22, 51)( 23, 50)( 24, 52)
( 25, 93)( 26, 95)( 27, 94)( 28, 96)( 29, 89)( 30, 91)( 31, 90)( 32, 92)
( 33, 85)( 34, 87)( 35, 86)( 36, 88)( 37, 81)( 38, 83)( 39, 82)( 40, 84)
( 41, 77)( 42, 79)( 43, 78)( 44, 80)( 45, 73)( 46, 75)( 47, 74)( 48, 76)
( 97,165)( 98,167)( 99,166)(100,168)(101,161)(102,163)(103,162)(104,164)
(105,157)(106,159)(107,158)(108,160)(109,153)(110,155)(111,154)(112,156)
(113,149)(114,151)(115,150)(116,152)(117,145)(118,147)(119,146)(120,148)
(121,189)(122,191)(123,190)(124,192)(125,185)(126,187)(127,186)(128,188)
(129,181)(130,183)(131,182)(132,184)(133,177)(134,179)(135,178)(136,180)
(137,173)(138,175)(139,174)(140,176)(141,169)(142,171)(143,170)(144,172)
(193,261)(194,263)(195,262)(196,264)(197,257)(198,259)(199,258)(200,260)
(201,253)(202,255)(203,254)(204,256)(205,249)(206,251)(207,250)(208,252)
(209,245)(210,247)(211,246)(212,248)(213,241)(214,243)(215,242)(216,244)
(217,285)(218,287)(219,286)(220,288)(221,281)(222,283)(223,282)(224,284)
(225,277)(226,279)(227,278)(228,280)(229,273)(230,275)(231,274)(232,276)
(233,269)(234,271)(235,270)(236,272)(237,265)(238,267)(239,266)(240,268)
(289,357)(290,359)(291,358)(292,360)(293,353)(294,355)(295,354)(296,356)
(297,349)(298,351)(299,350)(300,352)(301,345)(302,347)(303,346)(304,348)
(305,341)(306,343)(307,342)(308,344)(309,337)(310,339)(311,338)(312,340)
(313,381)(314,383)(315,382)(316,384)(317,377)(318,379)(319,378)(320,380)
(321,373)(322,375)(323,374)(324,376)(325,369)(326,371)(327,370)(328,372)
(329,365)(330,367)(331,366)(332,368)(333,361)(334,363)(335,362)(336,364);;
s3 := ( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)
( 9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,111)( 16,112)
( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)( 24,120)
( 25,121)( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)
( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)( 40,136)
( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)( 48,144)
( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)
( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)
( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)
( 73,145)( 74,146)( 75,147)( 76,148)( 77,149)( 78,150)( 79,151)( 80,152)
( 81,153)( 82,154)( 83,155)( 84,156)( 85,157)( 86,158)( 87,159)( 88,160)
( 89,161)( 90,162)( 91,163)( 92,164)( 93,165)( 94,166)( 95,167)( 96,168)
(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)(200,296)
(201,297)(202,298)(203,299)(204,300)(205,301)(206,302)(207,303)(208,304)
(209,305)(210,306)(211,307)(212,308)(213,309)(214,310)(215,311)(216,312)
(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)(224,320)
(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)(232,328)
(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)(240,336)
(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)(248,368)
(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)(256,376)
(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)
(265,337)(266,338)(267,339)(268,340)(269,341)(270,342)(271,343)(272,344)
(273,345)(274,346)(275,347)(276,348)(277,349)(278,350)(279,351)(280,352)
(281,353)(282,354)(283,355)(284,356)(285,357)(286,358)(287,359)(288,360);;
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*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1,196)( 2,195)( 3,194)( 4,193)( 5,200)( 6,199)( 7,198)
( 8,197)( 9,204)( 10,203)( 11,202)( 12,201)( 13,208)( 14,207)( 15,206)
( 16,205)( 17,212)( 18,211)( 19,210)( 20,209)( 21,216)( 22,215)( 23,214)
( 24,213)( 25,220)( 26,219)( 27,218)( 28,217)( 29,224)( 30,223)( 31,222)
( 32,221)( 33,228)( 34,227)( 35,226)( 36,225)( 37,232)( 38,231)( 39,230)
( 40,229)( 41,236)( 42,235)( 43,234)( 44,233)( 45,240)( 46,239)( 47,238)
( 48,237)( 49,244)( 50,243)( 51,242)( 52,241)( 53,248)( 54,247)( 55,246)
( 56,245)( 57,252)( 58,251)( 59,250)( 60,249)( 61,256)( 62,255)( 63,254)
( 64,253)( 65,260)( 66,259)( 67,258)( 68,257)( 69,264)( 70,263)( 71,262)
( 72,261)( 73,268)( 74,267)( 75,266)( 76,265)( 77,272)( 78,271)( 79,270)
( 80,269)( 81,276)( 82,275)( 83,274)( 84,273)( 85,280)( 86,279)( 87,278)
( 88,277)( 89,284)( 90,283)( 91,282)( 92,281)( 93,288)( 94,287)( 95,286)
( 96,285)( 97,292)( 98,291)( 99,290)(100,289)(101,296)(102,295)(103,294)
(104,293)(105,300)(106,299)(107,298)(108,297)(109,304)(110,303)(111,302)
(112,301)(113,308)(114,307)(115,306)(116,305)(117,312)(118,311)(119,310)
(120,309)(121,316)(122,315)(123,314)(124,313)(125,320)(126,319)(127,318)
(128,317)(129,324)(130,323)(131,322)(132,321)(133,328)(134,327)(135,326)
(136,325)(137,332)(138,331)(139,330)(140,329)(141,336)(142,335)(143,334)
(144,333)(145,340)(146,339)(147,338)(148,337)(149,344)(150,343)(151,342)
(152,341)(153,348)(154,347)(155,346)(156,345)(157,352)(158,351)(159,350)
(160,349)(161,356)(162,355)(163,354)(164,353)(165,360)(166,359)(167,358)
(168,357)(169,364)(170,363)(171,362)(172,361)(173,368)(174,367)(175,366)
(176,365)(177,372)(178,371)(179,370)(180,369)(181,376)(182,375)(183,374)
(184,373)(185,380)(186,379)(187,378)(188,377)(189,384)(190,383)(191,382)
(192,381);
s1 := Sym(384)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)
( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)
( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 61)( 50, 62)( 51, 64)
( 52, 63)( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 65)( 58, 66)( 59, 68)
( 60, 67)( 73, 85)( 74, 86)( 75, 88)( 76, 87)( 77, 93)( 78, 94)( 79, 96)
( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 99,100)(101,105)(102,106)
(103,108)(104,107)(111,112)(113,117)(114,118)(115,120)(116,119)(123,124)
(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)(139,144)
(140,143)(145,157)(146,158)(147,160)(148,159)(149,165)(150,166)(151,168)
(152,167)(153,161)(154,162)(155,164)(156,163)(169,181)(170,182)(171,184)
(172,183)(173,189)(174,190)(175,192)(176,191)(177,185)(178,186)(179,188)
(180,187)(195,196)(197,201)(198,202)(199,204)(200,203)(207,208)(209,213)
(210,214)(211,216)(212,215)(219,220)(221,225)(222,226)(223,228)(224,227)
(231,232)(233,237)(234,238)(235,240)(236,239)(241,253)(242,254)(243,256)
(244,255)(245,261)(246,262)(247,264)(248,263)(249,257)(250,258)(251,260)
(252,259)(265,277)(266,278)(267,280)(268,279)(269,285)(270,286)(271,288)
(272,287)(273,281)(274,282)(275,284)(276,283)(291,292)(293,297)(294,298)
(295,300)(296,299)(303,304)(305,309)(306,310)(307,312)(308,311)(315,316)
(317,321)(318,322)(319,324)(320,323)(327,328)(329,333)(330,334)(331,336)
(332,335)(337,349)(338,350)(339,352)(340,351)(341,357)(342,358)(343,360)
(344,359)(345,353)(346,354)(347,356)(348,355)(361,373)(362,374)(363,376)
(364,375)(365,381)(366,382)(367,384)(368,383)(369,377)(370,378)(371,380)
(372,379);
s2 := Sym(384)!( 1, 69)( 2, 71)( 3, 70)( 4, 72)( 5, 65)( 6, 67)( 7, 66)
( 8, 68)( 9, 61)( 10, 63)( 11, 62)( 12, 64)( 13, 57)( 14, 59)( 15, 58)
( 16, 60)( 17, 53)( 18, 55)( 19, 54)( 20, 56)( 21, 49)( 22, 51)( 23, 50)
( 24, 52)( 25, 93)( 26, 95)( 27, 94)( 28, 96)( 29, 89)( 30, 91)( 31, 90)
( 32, 92)( 33, 85)( 34, 87)( 35, 86)( 36, 88)( 37, 81)( 38, 83)( 39, 82)
( 40, 84)( 41, 77)( 42, 79)( 43, 78)( 44, 80)( 45, 73)( 46, 75)( 47, 74)
( 48, 76)( 97,165)( 98,167)( 99,166)(100,168)(101,161)(102,163)(103,162)
(104,164)(105,157)(106,159)(107,158)(108,160)(109,153)(110,155)(111,154)
(112,156)(113,149)(114,151)(115,150)(116,152)(117,145)(118,147)(119,146)
(120,148)(121,189)(122,191)(123,190)(124,192)(125,185)(126,187)(127,186)
(128,188)(129,181)(130,183)(131,182)(132,184)(133,177)(134,179)(135,178)
(136,180)(137,173)(138,175)(139,174)(140,176)(141,169)(142,171)(143,170)
(144,172)(193,261)(194,263)(195,262)(196,264)(197,257)(198,259)(199,258)
(200,260)(201,253)(202,255)(203,254)(204,256)(205,249)(206,251)(207,250)
(208,252)(209,245)(210,247)(211,246)(212,248)(213,241)(214,243)(215,242)
(216,244)(217,285)(218,287)(219,286)(220,288)(221,281)(222,283)(223,282)
(224,284)(225,277)(226,279)(227,278)(228,280)(229,273)(230,275)(231,274)
(232,276)(233,269)(234,271)(235,270)(236,272)(237,265)(238,267)(239,266)
(240,268)(289,357)(290,359)(291,358)(292,360)(293,353)(294,355)(295,354)
(296,356)(297,349)(298,351)(299,350)(300,352)(301,345)(302,347)(303,346)
(304,348)(305,341)(306,343)(307,342)(308,344)(309,337)(310,339)(311,338)
(312,340)(313,381)(314,383)(315,382)(316,384)(317,377)(318,379)(319,378)
(320,380)(321,373)(322,375)(323,374)(324,376)(325,369)(326,371)(327,370)
(328,372)(329,365)(330,367)(331,366)(332,368)(333,361)(334,363)(335,362)
(336,364);
s3 := Sym(384)!( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)
( 8,104)( 9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,111)
( 16,112)( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)
( 24,120)( 25,121)( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)
( 32,128)( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)
( 40,136)( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)
( 48,144)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)
( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)
( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)
( 72,192)( 73,145)( 74,146)( 75,147)( 76,148)( 77,149)( 78,150)( 79,151)
( 80,152)( 81,153)( 82,154)( 83,155)( 84,156)( 85,157)( 86,158)( 87,159)
( 88,160)( 89,161)( 90,162)( 91,163)( 92,164)( 93,165)( 94,166)( 95,167)
( 96,168)(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)
(200,296)(201,297)(202,298)(203,299)(204,300)(205,301)(206,302)(207,303)
(208,304)(209,305)(210,306)(211,307)(212,308)(213,309)(214,310)(215,311)
(216,312)(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)
(224,320)(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)
(232,328)(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)
(240,336)(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)
(248,368)(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)
(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)
(264,384)(265,337)(266,338)(267,339)(268,340)(269,341)(270,342)(271,343)
(272,344)(273,345)(274,346)(275,347)(276,348)(277,349)(278,350)(279,351)
(280,352)(281,353)(282,354)(283,355)(284,356)(285,357)(286,358)(287,359)
(288,360);
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*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope