Polytope of Type {12,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,155788)
Rank : 4
Schlafli Type : {12,12,3}
Number of vertices, edges, etc : 12, 96, 24, 4
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 : {12,6,3}*576, {6,12,3}*576
3-fold quotients : {4,12,3}*384
4-fold quotients : {6,6,3}*288
6-fold quotients : {4,6,3}*192, {2,12,3}*192
12-fold quotients : {2,6,3}*96
24-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)
(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)(160,240)
(161,225)(162,226)(163,227)(164,228)(165,229)(166,230)(167,231)(168,232)
(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)
(177,257)(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)(184,264)
(185,249)(186,250)(187,251)(188,252)(189,253)(190,254)(191,255)(192,256)
(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)
(201,281)(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)(208,288)
(209,273)(210,274)(211,275)(212,276)(213,277)(214,278)(215,279)(216,280);;
s1 := ( 1,153)( 2,154)( 3,156)( 4,155)( 5,159)( 6,160)( 7,157)( 8,158)
( 9,145)( 10,146)( 11,148)( 12,147)( 13,151)( 14,152)( 15,149)( 16,150)
( 17,161)( 18,162)( 19,164)( 20,163)( 21,167)( 22,168)( 23,165)( 24,166)
( 25,201)( 26,202)( 27,204)( 28,203)( 29,207)( 30,208)( 31,205)( 32,206)
( 33,193)( 34,194)( 35,196)( 36,195)( 37,199)( 38,200)( 39,197)( 40,198)
( 41,209)( 42,210)( 43,212)( 44,211)( 45,215)( 46,216)( 47,213)( 48,214)
( 49,177)( 50,178)( 51,180)( 52,179)( 53,183)( 54,184)( 55,181)( 56,182)
( 57,169)( 58,170)( 59,172)( 60,171)( 61,175)( 62,176)( 63,173)( 64,174)
( 65,185)( 66,186)( 67,188)( 68,187)( 69,191)( 70,192)( 71,189)( 72,190)
( 73,225)( 74,226)( 75,228)( 76,227)( 77,231)( 78,232)( 79,229)( 80,230)
( 81,217)( 82,218)( 83,220)( 84,219)( 85,223)( 86,224)( 87,221)( 88,222)
( 89,233)( 90,234)( 91,236)( 92,235)( 93,239)( 94,240)( 95,237)( 96,238)
( 97,273)( 98,274)( 99,276)(100,275)(101,279)(102,280)(103,277)(104,278)
(105,265)(106,266)(107,268)(108,267)(109,271)(110,272)(111,269)(112,270)
(113,281)(114,282)(115,284)(116,283)(117,287)(118,288)(119,285)(120,286)
(121,249)(122,250)(123,252)(124,251)(125,255)(126,256)(127,253)(128,254)
(129,241)(130,242)(131,244)(132,243)(133,247)(134,248)(135,245)(136,246)
(137,257)(138,258)(139,260)(140,259)(141,263)(142,264)(143,261)(144,262);;
s2 := ( 1, 25)( 2, 26)( 3, 31)( 4, 32)( 5, 30)( 6, 29)( 7, 27)( 8, 28)
( 9, 33)( 10, 34)( 11, 39)( 12, 40)( 13, 38)( 14, 37)( 15, 35)( 16, 36)
( 17, 41)( 18, 42)( 19, 47)( 20, 48)( 21, 46)( 22, 45)( 23, 43)( 24, 44)
( 51, 55)( 52, 56)( 53, 54)( 59, 63)( 60, 64)( 61, 62)( 67, 71)( 68, 72)
( 69, 70)( 73, 97)( 74, 98)( 75,103)( 76,104)( 77,102)( 78,101)( 79, 99)
( 80,100)( 81,105)( 82,106)( 83,111)( 84,112)( 85,110)( 86,109)( 87,107)
( 88,108)( 89,113)( 90,114)( 91,119)( 92,120)( 93,118)( 94,117)( 95,115)
( 96,116)(123,127)(124,128)(125,126)(131,135)(132,136)(133,134)(139,143)
(140,144)(141,142)(145,170)(146,169)(147,176)(148,175)(149,173)(150,174)
(151,172)(152,171)(153,178)(154,177)(155,184)(156,183)(157,181)(158,182)
(159,180)(160,179)(161,186)(162,185)(163,192)(164,191)(165,189)(166,190)
(167,188)(168,187)(193,194)(195,200)(196,199)(201,202)(203,208)(204,207)
(209,210)(211,216)(212,215)(217,242)(218,241)(219,248)(220,247)(221,245)
(222,246)(223,244)(224,243)(225,250)(226,249)(227,256)(228,255)(229,253)
(230,254)(231,252)(232,251)(233,258)(234,257)(235,264)(236,263)(237,261)
(238,262)(239,260)(240,259)(265,266)(267,272)(268,271)(273,274)(275,280)
(276,279)(281,282)(283,288)(284,287);;
s3 := ( 1, 3)( 2, 4)( 5, 6)( 9, 11)( 10, 12)( 13, 14)( 17, 19)( 18, 20)
( 21, 22)( 25, 51)( 26, 52)( 27, 49)( 28, 50)( 29, 54)( 30, 53)( 31, 55)
( 32, 56)( 33, 59)( 34, 60)( 35, 57)( 36, 58)( 37, 62)( 38, 61)( 39, 63)
( 40, 64)( 41, 67)( 42, 68)( 43, 65)( 44, 66)( 45, 70)( 46, 69)( 47, 71)
( 48, 72)( 73, 75)( 74, 76)( 77, 78)( 81, 83)( 82, 84)( 85, 86)( 89, 91)
( 90, 92)( 93, 94)( 97,123)( 98,124)( 99,121)(100,122)(101,126)(102,125)
(103,127)(104,128)(105,131)(106,132)(107,129)(108,130)(109,134)(110,133)
(111,135)(112,136)(113,139)(114,140)(115,137)(116,138)(117,142)(118,141)
(119,143)(120,144)(145,148)(146,147)(151,152)(153,156)(154,155)(159,160)
(161,164)(162,163)(167,168)(169,196)(170,195)(171,194)(172,193)(173,197)
(174,198)(175,200)(176,199)(177,204)(178,203)(179,202)(180,201)(181,205)
(182,206)(183,208)(184,207)(185,212)(186,211)(187,210)(188,209)(189,213)
(190,214)(191,216)(192,215)(217,220)(218,219)(223,224)(225,228)(226,227)
(231,232)(233,236)(234,235)(239,240)(241,268)(242,267)(243,266)(244,265)
(245,269)(246,270)(247,272)(248,271)(249,276)(250,275)(251,274)(252,273)
(253,277)(254,278)(255,280)(256,279)(257,284)(258,283)(259,282)(260,281)
(261,285)(262,286)(263,288)(264,287);;
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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)
( 16, 24)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)
( 64, 72)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)
(112,120)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)
(152,224)(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)
(160,240)(161,225)(162,226)(163,227)(164,228)(165,229)(166,230)(167,231)
(168,232)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)
(176,248)(177,257)(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)
(184,264)(185,249)(186,250)(187,251)(188,252)(189,253)(190,254)(191,255)
(192,256)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)
(200,272)(201,281)(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)
(208,288)(209,273)(210,274)(211,275)(212,276)(213,277)(214,278)(215,279)
(216,280);
s1 := Sym(288)!( 1,153)( 2,154)( 3,156)( 4,155)( 5,159)( 6,160)( 7,157)
( 8,158)( 9,145)( 10,146)( 11,148)( 12,147)( 13,151)( 14,152)( 15,149)
( 16,150)( 17,161)( 18,162)( 19,164)( 20,163)( 21,167)( 22,168)( 23,165)
( 24,166)( 25,201)( 26,202)( 27,204)( 28,203)( 29,207)( 30,208)( 31,205)
( 32,206)( 33,193)( 34,194)( 35,196)( 36,195)( 37,199)( 38,200)( 39,197)
( 40,198)( 41,209)( 42,210)( 43,212)( 44,211)( 45,215)( 46,216)( 47,213)
( 48,214)( 49,177)( 50,178)( 51,180)( 52,179)( 53,183)( 54,184)( 55,181)
( 56,182)( 57,169)( 58,170)( 59,172)( 60,171)( 61,175)( 62,176)( 63,173)
( 64,174)( 65,185)( 66,186)( 67,188)( 68,187)( 69,191)( 70,192)( 71,189)
( 72,190)( 73,225)( 74,226)( 75,228)( 76,227)( 77,231)( 78,232)( 79,229)
( 80,230)( 81,217)( 82,218)( 83,220)( 84,219)( 85,223)( 86,224)( 87,221)
( 88,222)( 89,233)( 90,234)( 91,236)( 92,235)( 93,239)( 94,240)( 95,237)
( 96,238)( 97,273)( 98,274)( 99,276)(100,275)(101,279)(102,280)(103,277)
(104,278)(105,265)(106,266)(107,268)(108,267)(109,271)(110,272)(111,269)
(112,270)(113,281)(114,282)(115,284)(116,283)(117,287)(118,288)(119,285)
(120,286)(121,249)(122,250)(123,252)(124,251)(125,255)(126,256)(127,253)
(128,254)(129,241)(130,242)(131,244)(132,243)(133,247)(134,248)(135,245)
(136,246)(137,257)(138,258)(139,260)(140,259)(141,263)(142,264)(143,261)
(144,262);
s2 := Sym(288)!( 1, 25)( 2, 26)( 3, 31)( 4, 32)( 5, 30)( 6, 29)( 7, 27)
( 8, 28)( 9, 33)( 10, 34)( 11, 39)( 12, 40)( 13, 38)( 14, 37)( 15, 35)
( 16, 36)( 17, 41)( 18, 42)( 19, 47)( 20, 48)( 21, 46)( 22, 45)( 23, 43)
( 24, 44)( 51, 55)( 52, 56)( 53, 54)( 59, 63)( 60, 64)( 61, 62)( 67, 71)
( 68, 72)( 69, 70)( 73, 97)( 74, 98)( 75,103)( 76,104)( 77,102)( 78,101)
( 79, 99)( 80,100)( 81,105)( 82,106)( 83,111)( 84,112)( 85,110)( 86,109)
( 87,107)( 88,108)( 89,113)( 90,114)( 91,119)( 92,120)( 93,118)( 94,117)
( 95,115)( 96,116)(123,127)(124,128)(125,126)(131,135)(132,136)(133,134)
(139,143)(140,144)(141,142)(145,170)(146,169)(147,176)(148,175)(149,173)
(150,174)(151,172)(152,171)(153,178)(154,177)(155,184)(156,183)(157,181)
(158,182)(159,180)(160,179)(161,186)(162,185)(163,192)(164,191)(165,189)
(166,190)(167,188)(168,187)(193,194)(195,200)(196,199)(201,202)(203,208)
(204,207)(209,210)(211,216)(212,215)(217,242)(218,241)(219,248)(220,247)
(221,245)(222,246)(223,244)(224,243)(225,250)(226,249)(227,256)(228,255)
(229,253)(230,254)(231,252)(232,251)(233,258)(234,257)(235,264)(236,263)
(237,261)(238,262)(239,260)(240,259)(265,266)(267,272)(268,271)(273,274)
(275,280)(276,279)(281,282)(283,288)(284,287);
s3 := Sym(288)!( 1, 3)( 2, 4)( 5, 6)( 9, 11)( 10, 12)( 13, 14)( 17, 19)
( 18, 20)( 21, 22)( 25, 51)( 26, 52)( 27, 49)( 28, 50)( 29, 54)( 30, 53)
( 31, 55)( 32, 56)( 33, 59)( 34, 60)( 35, 57)( 36, 58)( 37, 62)( 38, 61)
( 39, 63)( 40, 64)( 41, 67)( 42, 68)( 43, 65)( 44, 66)( 45, 70)( 46, 69)
( 47, 71)( 48, 72)( 73, 75)( 74, 76)( 77, 78)( 81, 83)( 82, 84)( 85, 86)
( 89, 91)( 90, 92)( 93, 94)( 97,123)( 98,124)( 99,121)(100,122)(101,126)
(102,125)(103,127)(104,128)(105,131)(106,132)(107,129)(108,130)(109,134)
(110,133)(111,135)(112,136)(113,139)(114,140)(115,137)(116,138)(117,142)
(118,141)(119,143)(120,144)(145,148)(146,147)(151,152)(153,156)(154,155)
(159,160)(161,164)(162,163)(167,168)(169,196)(170,195)(171,194)(172,193)
(173,197)(174,198)(175,200)(176,199)(177,204)(178,203)(179,202)(180,201)
(181,205)(182,206)(183,208)(184,207)(185,212)(186,211)(187,210)(188,209)
(189,213)(190,214)(191,216)(192,215)(217,220)(218,219)(223,224)(225,228)
(226,227)(231,232)(233,236)(234,235)(239,240)(241,268)(242,267)(243,266)
(244,265)(245,269)(246,270)(247,272)(248,271)(249,276)(250,275)(251,274)
(252,273)(253,277)(254,278)(255,280)(256,279)(257,284)(258,283)(259,282)
(260,281)(261,285)(262,286)(263,288)(264,287);
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,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope