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