Polytope of Type {3,12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12,8}*1152
if this polytope has a name.
Group : SmallGroup(1152,156074)
Rank : 4
Schlafli Type : {3,12,8}
Number of vertices, edges, etc : 6, 36, 96, 8
Order of s0s1s2s3 : 24
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 : {3,12,4}*576
3-fold quotients : {3,4,8}*384
4-fold quotients : {3,6,8}*288, {3,12,2}*288
6-fold quotients : {3,4,4}*192b
8-fold quotients : {3,6,4}*144
12-fold quotients : {3,2,8}*96, {3,4,2}*96
16-fold quotients : {3,6,2}*72
24-fold quotients : {3,2,4}*48, {3,4,2}*48
48-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 25)( 14, 26)( 15, 28)
( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)( 23, 32)
( 24, 31)( 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)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 85, 97)
( 86, 98)( 87,100)( 88, 99)( 89,105)( 90,106)( 91,108)( 92,107)( 93,101)
( 94,102)( 95,104)( 96,103)(111,112)(113,117)(114,118)(115,120)(116,119)
(121,133)(122,134)(123,136)(124,135)(125,141)(126,142)(127,144)(128,143)
(129,137)(130,138)(131,140)(132,139)(147,148)(149,153)(150,154)(151,156)
(152,155)(157,169)(158,170)(159,172)(160,171)(161,177)(162,178)(163,180)
(164,179)(165,173)(166,174)(167,176)(168,175)(183,184)(185,189)(186,190)
(187,192)(188,191)(193,205)(194,206)(195,208)(196,207)(197,213)(198,214)
(199,216)(200,215)(201,209)(202,210)(203,212)(204,211)(219,220)(221,225)
(222,226)(223,228)(224,227)(229,241)(230,242)(231,244)(232,243)(233,249)
(234,250)(235,252)(236,251)(237,245)(238,246)(239,248)(240,247)(255,256)
(257,261)(258,262)(259,264)(260,263)(265,277)(266,278)(267,280)(268,279)
(269,285)(270,286)(271,288)(272,287)(273,281)(274,282)(275,284)(276,283);;
s1 := ( 1, 17)( 2, 20)( 3, 19)( 4, 18)( 5, 13)( 6, 16)( 7, 15)( 8, 14)
( 9, 21)( 10, 24)( 11, 23)( 12, 22)( 25, 29)( 26, 32)( 27, 31)( 28, 30)
( 34, 36)( 37, 53)( 38, 56)( 39, 55)( 40, 54)( 41, 49)( 42, 52)( 43, 51)
( 44, 50)( 45, 57)( 46, 60)( 47, 59)( 48, 58)( 61, 65)( 62, 68)( 63, 67)
( 64, 66)( 70, 72)( 73, 89)( 74, 92)( 75, 91)( 76, 90)( 77, 85)( 78, 88)
( 79, 87)( 80, 86)( 81, 93)( 82, 96)( 83, 95)( 84, 94)( 97,101)( 98,104)
( 99,103)(100,102)(106,108)(109,125)(110,128)(111,127)(112,126)(113,121)
(114,124)(115,123)(116,122)(117,129)(118,132)(119,131)(120,130)(133,137)
(134,140)(135,139)(136,138)(142,144)(145,161)(146,164)(147,163)(148,162)
(149,157)(150,160)(151,159)(152,158)(153,165)(154,168)(155,167)(156,166)
(169,173)(170,176)(171,175)(172,174)(178,180)(181,197)(182,200)(183,199)
(184,198)(185,193)(186,196)(187,195)(188,194)(189,201)(190,204)(191,203)
(192,202)(205,209)(206,212)(207,211)(208,210)(214,216)(217,233)(218,236)
(219,235)(220,234)(221,229)(222,232)(223,231)(224,230)(225,237)(226,240)
(227,239)(228,238)(241,245)(242,248)(243,247)(244,246)(250,252)(253,269)
(254,272)(255,271)(256,270)(257,265)(258,268)(259,267)(260,266)(261,273)
(262,276)(263,275)(264,274)(277,281)(278,284)(279,283)(280,282)(286,288);;
s2 := ( 1, 2)( 3, 4)( 5, 10)( 6, 9)( 7, 12)( 8, 11)( 13, 14)( 15, 16)
( 17, 22)( 18, 21)( 19, 24)( 20, 23)( 25, 26)( 27, 28)( 29, 34)( 30, 33)
( 31, 36)( 32, 35)( 37, 38)( 39, 40)( 41, 46)( 42, 45)( 43, 48)( 44, 47)
( 49, 50)( 51, 52)( 53, 58)( 54, 57)( 55, 60)( 56, 59)( 61, 62)( 63, 64)
( 65, 70)( 66, 69)( 67, 72)( 68, 71)( 73,110)( 74,109)( 75,112)( 76,111)
( 77,118)( 78,117)( 79,120)( 80,119)( 81,114)( 82,113)( 83,116)( 84,115)
( 85,122)( 86,121)( 87,124)( 88,123)( 89,130)( 90,129)( 91,132)( 92,131)
( 93,126)( 94,125)( 95,128)( 96,127)( 97,134)( 98,133)( 99,136)(100,135)
(101,142)(102,141)(103,144)(104,143)(105,138)(106,137)(107,140)(108,139)
(145,218)(146,217)(147,220)(148,219)(149,226)(150,225)(151,228)(152,227)
(153,222)(154,221)(155,224)(156,223)(157,230)(158,229)(159,232)(160,231)
(161,238)(162,237)(163,240)(164,239)(165,234)(166,233)(167,236)(168,235)
(169,242)(170,241)(171,244)(172,243)(173,250)(174,249)(175,252)(176,251)
(177,246)(178,245)(179,248)(180,247)(181,254)(182,253)(183,256)(184,255)
(185,262)(186,261)(187,264)(188,263)(189,258)(190,257)(191,260)(192,259)
(193,266)(194,265)(195,268)(196,267)(197,274)(198,273)(199,276)(200,275)
(201,270)(202,269)(203,272)(204,271)(205,278)(206,277)(207,280)(208,279)
(209,286)(210,285)(211,288)(212,287)(213,282)(214,281)(215,284)(216,283);;
s3 := ( 1,145)( 2,146)( 3,147)( 4,148)( 5,149)( 6,150)( 7,151)( 8,152)
( 9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)
( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)
( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)( 40,184)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)
( 73,253)( 74,254)( 75,255)( 76,256)( 77,257)( 78,258)( 79,259)( 80,260)
( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)( 88,268)
( 89,269)( 90,270)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)( 96,276)
( 97,277)( 98,278)( 99,279)(100,280)(101,281)(102,282)(103,283)(104,284)
(105,285)(106,286)(107,287)(108,288)(109,217)(110,218)(111,219)(112,220)
(113,221)(114,222)(115,223)(116,224)(117,225)(118,226)(119,227)(120,228)
(121,229)(122,230)(123,231)(124,232)(125,233)(126,234)(127,235)(128,236)
(129,237)(130,238)(131,239)(132,240)(133,241)(134,242)(135,243)(136,244)
(137,245)(138,246)(139,247)(140,248)(141,249)(142,250)(143,251)(144,252);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 25)( 14, 26)
( 15, 28)( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)
( 23, 32)( 24, 31)( 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)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)
( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,105)( 90,106)( 91,108)( 92,107)
( 93,101)( 94,102)( 95,104)( 96,103)(111,112)(113,117)(114,118)(115,120)
(116,119)(121,133)(122,134)(123,136)(124,135)(125,141)(126,142)(127,144)
(128,143)(129,137)(130,138)(131,140)(132,139)(147,148)(149,153)(150,154)
(151,156)(152,155)(157,169)(158,170)(159,172)(160,171)(161,177)(162,178)
(163,180)(164,179)(165,173)(166,174)(167,176)(168,175)(183,184)(185,189)
(186,190)(187,192)(188,191)(193,205)(194,206)(195,208)(196,207)(197,213)
(198,214)(199,216)(200,215)(201,209)(202,210)(203,212)(204,211)(219,220)
(221,225)(222,226)(223,228)(224,227)(229,241)(230,242)(231,244)(232,243)
(233,249)(234,250)(235,252)(236,251)(237,245)(238,246)(239,248)(240,247)
(255,256)(257,261)(258,262)(259,264)(260,263)(265,277)(266,278)(267,280)
(268,279)(269,285)(270,286)(271,288)(272,287)(273,281)(274,282)(275,284)
(276,283);
s1 := Sym(288)!( 1, 17)( 2, 20)( 3, 19)( 4, 18)( 5, 13)( 6, 16)( 7, 15)
( 8, 14)( 9, 21)( 10, 24)( 11, 23)( 12, 22)( 25, 29)( 26, 32)( 27, 31)
( 28, 30)( 34, 36)( 37, 53)( 38, 56)( 39, 55)( 40, 54)( 41, 49)( 42, 52)
( 43, 51)( 44, 50)( 45, 57)( 46, 60)( 47, 59)( 48, 58)( 61, 65)( 62, 68)
( 63, 67)( 64, 66)( 70, 72)( 73, 89)( 74, 92)( 75, 91)( 76, 90)( 77, 85)
( 78, 88)( 79, 87)( 80, 86)( 81, 93)( 82, 96)( 83, 95)( 84, 94)( 97,101)
( 98,104)( 99,103)(100,102)(106,108)(109,125)(110,128)(111,127)(112,126)
(113,121)(114,124)(115,123)(116,122)(117,129)(118,132)(119,131)(120,130)
(133,137)(134,140)(135,139)(136,138)(142,144)(145,161)(146,164)(147,163)
(148,162)(149,157)(150,160)(151,159)(152,158)(153,165)(154,168)(155,167)
(156,166)(169,173)(170,176)(171,175)(172,174)(178,180)(181,197)(182,200)
(183,199)(184,198)(185,193)(186,196)(187,195)(188,194)(189,201)(190,204)
(191,203)(192,202)(205,209)(206,212)(207,211)(208,210)(214,216)(217,233)
(218,236)(219,235)(220,234)(221,229)(222,232)(223,231)(224,230)(225,237)
(226,240)(227,239)(228,238)(241,245)(242,248)(243,247)(244,246)(250,252)
(253,269)(254,272)(255,271)(256,270)(257,265)(258,268)(259,267)(260,266)
(261,273)(262,276)(263,275)(264,274)(277,281)(278,284)(279,283)(280,282)
(286,288);
s2 := Sym(288)!( 1, 2)( 3, 4)( 5, 10)( 6, 9)( 7, 12)( 8, 11)( 13, 14)
( 15, 16)( 17, 22)( 18, 21)( 19, 24)( 20, 23)( 25, 26)( 27, 28)( 29, 34)
( 30, 33)( 31, 36)( 32, 35)( 37, 38)( 39, 40)( 41, 46)( 42, 45)( 43, 48)
( 44, 47)( 49, 50)( 51, 52)( 53, 58)( 54, 57)( 55, 60)( 56, 59)( 61, 62)
( 63, 64)( 65, 70)( 66, 69)( 67, 72)( 68, 71)( 73,110)( 74,109)( 75,112)
( 76,111)( 77,118)( 78,117)( 79,120)( 80,119)( 81,114)( 82,113)( 83,116)
( 84,115)( 85,122)( 86,121)( 87,124)( 88,123)( 89,130)( 90,129)( 91,132)
( 92,131)( 93,126)( 94,125)( 95,128)( 96,127)( 97,134)( 98,133)( 99,136)
(100,135)(101,142)(102,141)(103,144)(104,143)(105,138)(106,137)(107,140)
(108,139)(145,218)(146,217)(147,220)(148,219)(149,226)(150,225)(151,228)
(152,227)(153,222)(154,221)(155,224)(156,223)(157,230)(158,229)(159,232)
(160,231)(161,238)(162,237)(163,240)(164,239)(165,234)(166,233)(167,236)
(168,235)(169,242)(170,241)(171,244)(172,243)(173,250)(174,249)(175,252)
(176,251)(177,246)(178,245)(179,248)(180,247)(181,254)(182,253)(183,256)
(184,255)(185,262)(186,261)(187,264)(188,263)(189,258)(190,257)(191,260)
(192,259)(193,266)(194,265)(195,268)(196,267)(197,274)(198,273)(199,276)
(200,275)(201,270)(202,269)(203,272)(204,271)(205,278)(206,277)(207,280)
(208,279)(209,286)(210,285)(211,288)(212,287)(213,282)(214,281)(215,284)
(216,283);
s3 := Sym(288)!( 1,145)( 2,146)( 3,147)( 4,148)( 5,149)( 6,150)( 7,151)
( 8,152)( 9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)
( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)
( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)
( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)
( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)
( 48,192)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)
( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)
( 72,216)( 73,253)( 74,254)( 75,255)( 76,256)( 77,257)( 78,258)( 79,259)
( 80,260)( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)
( 88,268)( 89,269)( 90,270)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)
( 96,276)( 97,277)( 98,278)( 99,279)(100,280)(101,281)(102,282)(103,283)
(104,284)(105,285)(106,286)(107,287)(108,288)(109,217)(110,218)(111,219)
(112,220)(113,221)(114,222)(115,223)(116,224)(117,225)(118,226)(119,227)
(120,228)(121,229)(122,230)(123,231)(124,232)(125,233)(126,234)(127,235)
(128,236)(129,237)(130,238)(131,239)(132,240)(133,241)(134,242)(135,243)
(136,244)(137,245)(138,246)(139,247)(140,248)(141,249)(142,250)(143,251)
(144,252);
poly := sub<Sym(288)|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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 >;
References : None.
to this polytope