Polytope of Type {12,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12,4}*1152f
if this polytope has a name.
Group : SmallGroup(1152,156063)
Rank : 4
Schlafli Type : {12,12,4}
Number of vertices, edges, etc : 12, 72, 24, 4
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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 : {6,12,4}*576f, {12,6,4}*576e
3-fold quotients : {4,12,4}*384b
4-fold quotients : {6,6,4}*288e
6-fold quotients : {2,12,4}*192b, {4,6,4}*192b
8-fold quotients : {6,3,4}*144
12-fold quotients : {2,6,4}*96c
24-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)
( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)
( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)(116,120)
(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)(140,144)
(145,181)(146,182)(147,183)(148,184)(149,189)(150,190)(151,191)(152,192)
(153,185)(154,186)(155,187)(156,188)(157,193)(158,194)(159,195)(160,196)
(161,201)(162,202)(163,203)(164,204)(165,197)(166,198)(167,199)(168,200)
(169,205)(170,206)(171,207)(172,208)(173,213)(174,214)(175,215)(176,216)
(177,209)(178,210)(179,211)(180,212)(217,253)(218,254)(219,255)(220,256)
(221,261)(222,262)(223,263)(224,264)(225,257)(226,258)(227,259)(228,260)
(229,265)(230,266)(231,267)(232,268)(233,273)(234,274)(235,275)(236,276)
(237,269)(238,270)(239,271)(240,272)(241,277)(242,278)(243,279)(244,280)
(245,285)(246,286)(247,287)(248,288)(249,281)(250,282)(251,283)(252,284);;
s1 := ( 1,149)( 2,150)( 3,152)( 4,151)( 5,145)( 6,146)( 7,148)( 8,147)
( 9,153)( 10,154)( 11,156)( 12,155)( 13,173)( 14,174)( 15,176)( 16,175)
( 17,169)( 18,170)( 19,172)( 20,171)( 21,177)( 22,178)( 23,180)( 24,179)
( 25,161)( 26,162)( 27,164)( 28,163)( 29,157)( 30,158)( 31,160)( 32,159)
( 33,165)( 34,166)( 35,168)( 36,167)( 37,185)( 38,186)( 39,188)( 40,187)
( 41,181)( 42,182)( 43,184)( 44,183)( 45,189)( 46,190)( 47,192)( 48,191)
( 49,209)( 50,210)( 51,212)( 52,211)( 53,205)( 54,206)( 55,208)( 56,207)
( 57,213)( 58,214)( 59,216)( 60,215)( 61,197)( 62,198)( 63,200)( 64,199)
( 65,193)( 66,194)( 67,196)( 68,195)( 69,201)( 70,202)( 71,204)( 72,203)
( 73,221)( 74,222)( 75,224)( 76,223)( 77,217)( 78,218)( 79,220)( 80,219)
( 81,225)( 82,226)( 83,228)( 84,227)( 85,245)( 86,246)( 87,248)( 88,247)
( 89,241)( 90,242)( 91,244)( 92,243)( 93,249)( 94,250)( 95,252)( 96,251)
( 97,233)( 98,234)( 99,236)(100,235)(101,229)(102,230)(103,232)(104,231)
(105,237)(106,238)(107,240)(108,239)(109,257)(110,258)(111,260)(112,259)
(113,253)(114,254)(115,256)(116,255)(117,261)(118,262)(119,264)(120,263)
(121,281)(122,282)(123,284)(124,283)(125,277)(126,278)(127,280)(128,279)
(129,285)(130,286)(131,288)(132,287)(133,269)(134,270)(135,272)(136,271)
(137,265)(138,266)(139,268)(140,267)(141,273)(142,274)(143,276)(144,275);;
s2 := ( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 21)( 6, 24)( 7, 23)( 8, 22)
( 9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)( 31, 35)
( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)( 43, 59)
( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)( 66, 72)
( 67, 71)( 68, 70)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)( 78, 96)
( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 98,100)(101,105)
(102,108)(103,107)(104,106)(109,121)(110,124)(111,123)(112,122)(113,129)
(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)(134,136)
(137,141)(138,144)(139,143)(140,142)(145,265)(146,268)(147,267)(148,266)
(149,273)(150,276)(151,275)(152,274)(153,269)(154,272)(155,271)(156,270)
(157,253)(158,256)(159,255)(160,254)(161,261)(162,264)(163,263)(164,262)
(165,257)(166,260)(167,259)(168,258)(169,277)(170,280)(171,279)(172,278)
(173,285)(174,288)(175,287)(176,286)(177,281)(178,284)(179,283)(180,282)
(181,229)(182,232)(183,231)(184,230)(185,237)(186,240)(187,239)(188,238)
(189,233)(190,236)(191,235)(192,234)(193,217)(194,220)(195,219)(196,218)
(197,225)(198,228)(199,227)(200,226)(201,221)(202,224)(203,223)(204,222)
(205,241)(206,244)(207,243)(208,242)(209,249)(210,252)(211,251)(212,250)
(213,245)(214,248)(215,247)(216,246);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288);;
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*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s2*s0*s1*s0*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*s0*s1*s0*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(288)!( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)
( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)
( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)
( 68, 72)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)
(116,120)(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)
(140,144)(145,181)(146,182)(147,183)(148,184)(149,189)(150,190)(151,191)
(152,192)(153,185)(154,186)(155,187)(156,188)(157,193)(158,194)(159,195)
(160,196)(161,201)(162,202)(163,203)(164,204)(165,197)(166,198)(167,199)
(168,200)(169,205)(170,206)(171,207)(172,208)(173,213)(174,214)(175,215)
(176,216)(177,209)(178,210)(179,211)(180,212)(217,253)(218,254)(219,255)
(220,256)(221,261)(222,262)(223,263)(224,264)(225,257)(226,258)(227,259)
(228,260)(229,265)(230,266)(231,267)(232,268)(233,273)(234,274)(235,275)
(236,276)(237,269)(238,270)(239,271)(240,272)(241,277)(242,278)(243,279)
(244,280)(245,285)(246,286)(247,287)(248,288)(249,281)(250,282)(251,283)
(252,284);
s1 := Sym(288)!( 1,149)( 2,150)( 3,152)( 4,151)( 5,145)( 6,146)( 7,148)
( 8,147)( 9,153)( 10,154)( 11,156)( 12,155)( 13,173)( 14,174)( 15,176)
( 16,175)( 17,169)( 18,170)( 19,172)( 20,171)( 21,177)( 22,178)( 23,180)
( 24,179)( 25,161)( 26,162)( 27,164)( 28,163)( 29,157)( 30,158)( 31,160)
( 32,159)( 33,165)( 34,166)( 35,168)( 36,167)( 37,185)( 38,186)( 39,188)
( 40,187)( 41,181)( 42,182)( 43,184)( 44,183)( 45,189)( 46,190)( 47,192)
( 48,191)( 49,209)( 50,210)( 51,212)( 52,211)( 53,205)( 54,206)( 55,208)
( 56,207)( 57,213)( 58,214)( 59,216)( 60,215)( 61,197)( 62,198)( 63,200)
( 64,199)( 65,193)( 66,194)( 67,196)( 68,195)( 69,201)( 70,202)( 71,204)
( 72,203)( 73,221)( 74,222)( 75,224)( 76,223)( 77,217)( 78,218)( 79,220)
( 80,219)( 81,225)( 82,226)( 83,228)( 84,227)( 85,245)( 86,246)( 87,248)
( 88,247)( 89,241)( 90,242)( 91,244)( 92,243)( 93,249)( 94,250)( 95,252)
( 96,251)( 97,233)( 98,234)( 99,236)(100,235)(101,229)(102,230)(103,232)
(104,231)(105,237)(106,238)(107,240)(108,239)(109,257)(110,258)(111,260)
(112,259)(113,253)(114,254)(115,256)(116,255)(117,261)(118,262)(119,264)
(120,263)(121,281)(122,282)(123,284)(124,283)(125,277)(126,278)(127,280)
(128,279)(129,285)(130,286)(131,288)(132,287)(133,269)(134,270)(135,272)
(136,271)(137,265)(138,266)(139,268)(140,267)(141,273)(142,274)(143,276)
(144,275);
s2 := Sym(288)!( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 21)( 6, 24)( 7, 23)
( 8, 22)( 9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)
( 31, 35)( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)
( 43, 59)( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)
( 66, 72)( 67, 71)( 68, 70)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)
( 78, 96)( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 98,100)
(101,105)(102,108)(103,107)(104,106)(109,121)(110,124)(111,123)(112,122)
(113,129)(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)
(134,136)(137,141)(138,144)(139,143)(140,142)(145,265)(146,268)(147,267)
(148,266)(149,273)(150,276)(151,275)(152,274)(153,269)(154,272)(155,271)
(156,270)(157,253)(158,256)(159,255)(160,254)(161,261)(162,264)(163,263)
(164,262)(165,257)(166,260)(167,259)(168,258)(169,277)(170,280)(171,279)
(172,278)(173,285)(174,288)(175,287)(176,286)(177,281)(178,284)(179,283)
(180,282)(181,229)(182,232)(183,231)(184,230)(185,237)(186,240)(187,239)
(188,238)(189,233)(190,236)(191,235)(192,234)(193,217)(194,220)(195,219)
(196,218)(197,225)(198,228)(199,227)(200,226)(201,221)(202,224)(203,223)
(204,222)(205,241)(206,244)(207,243)(208,242)(209,249)(210,252)(211,251)
(212,250)(213,245)(214,248)(215,247)(216,246);
s3 := Sym(288)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288);
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*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s2*s0*s1*s0*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*s0*s1*s0*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