Polytope of Type {12,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,6}*1152c
if this polytope has a name.
Group : SmallGroup(1152,157550)
Rank : 4
Schlafli Type : {12,4,6}
Number of vertices, edges, etc : 12, 48, 24, 12
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 : {12,4,3}*576, {6,4,6}*576a
3-fold quotients : {4,4,6}*384d
4-fold quotients : {12,2,6}*288, {6,4,3}*288
6-fold quotients : {4,4,3}*192b, {2,4,6}*192
8-fold quotients : {12,2,3}*144, {6,2,6}*144
12-fold quotients : {12,2,2}*96, {4,2,6}*96, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
16-fold quotients : {3,2,6}*72, {6,2,3}*72
24-fold quotients : {4,2,3}*48, {2,4,3}*48, {2,2,6}*48, {6,2,2}*48
32-fold quotients : {3,2,3}*36
36-fold quotients : {4,2,2}*32
48-fold quotients : {2,2,3}*24, {3,2,2}*24
72-fold quotients : {2,2,2}*16
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)
( 73,109)( 74,110)( 75,111)( 76,112)( 77,117)( 78,118)( 79,119)( 80,120)
( 81,113)( 82,114)( 83,115)( 84,116)( 85,121)( 86,122)( 87,123)( 88,124)
( 89,129)( 90,130)( 91,131)( 92,132)( 93,125)( 94,126)( 95,127)( 96,128)
( 97,133)( 98,134)( 99,135)(100,136)(101,141)(102,142)(103,143)(104,144)
(105,137)(106,138)(107,139)(108,140)(149,153)(150,154)(151,155)(152,156)
(161,165)(162,166)(163,167)(164,168)(173,177)(174,178)(175,179)(176,180)
(185,189)(186,190)(187,191)(188,192)(197,201)(198,202)(199,203)(200,204)
(209,213)(210,214)(211,215)(212,216)(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, 79)( 2, 80)( 3, 77)( 4, 78)( 5, 75)( 6, 76)( 7, 73)( 8, 74)
( 9, 83)( 10, 84)( 11, 81)( 12, 82)( 13, 91)( 14, 92)( 15, 89)( 16, 90)
( 17, 87)( 18, 88)( 19, 85)( 20, 86)( 21, 95)( 22, 96)( 23, 93)( 24, 94)
( 25,103)( 26,104)( 27,101)( 28,102)( 29, 99)( 30,100)( 31, 97)( 32, 98)
( 33,107)( 34,108)( 35,105)( 36,106)( 37,115)( 38,116)( 39,113)( 40,114)
( 41,111)( 42,112)( 43,109)( 44,110)( 45,119)( 46,120)( 47,117)( 48,118)
( 49,127)( 50,128)( 51,125)( 52,126)( 53,123)( 54,124)( 55,121)( 56,122)
( 57,131)( 58,132)( 59,129)( 60,130)( 61,139)( 62,140)( 63,137)( 64,138)
( 65,135)( 66,136)( 67,133)( 68,134)( 69,143)( 70,144)( 71,141)( 72,142)
(145,223)(146,224)(147,221)(148,222)(149,219)(150,220)(151,217)(152,218)
(153,227)(154,228)(155,225)(156,226)(157,235)(158,236)(159,233)(160,234)
(161,231)(162,232)(163,229)(164,230)(165,239)(166,240)(167,237)(168,238)
(169,247)(170,248)(171,245)(172,246)(173,243)(174,244)(175,241)(176,242)
(177,251)(178,252)(179,249)(180,250)(181,259)(182,260)(183,257)(184,258)
(185,255)(186,256)(187,253)(188,254)(189,263)(190,264)(191,261)(192,262)
(193,271)(194,272)(195,269)(196,270)(197,267)(198,268)(199,265)(200,266)
(201,275)(202,276)(203,273)(204,274)(205,283)(206,284)(207,281)(208,282)
(209,279)(210,280)(211,277)(212,278)(213,287)(214,288)(215,285)(216,286);;
s2 := ( 3, 4)( 7, 8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 29)
( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 39, 40)
( 43, 44)( 47, 48)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 65)( 54, 66)
( 55, 68)( 56, 67)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 75, 76)( 79, 80)
( 83, 84)( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,101)( 90,102)( 91,104)
( 92,103)( 93,105)( 94,106)( 95,108)( 96,107)(111,112)(115,116)(119,120)
(121,133)(122,134)(123,136)(124,135)(125,137)(126,138)(127,140)(128,139)
(129,141)(130,142)(131,144)(132,143)(147,148)(151,152)(155,156)(157,169)
(158,170)(159,172)(160,171)(161,173)(162,174)(163,176)(164,175)(165,177)
(166,178)(167,180)(168,179)(183,184)(187,188)(191,192)(193,205)(194,206)
(195,208)(196,207)(197,209)(198,210)(199,212)(200,211)(201,213)(202,214)
(203,216)(204,215)(219,220)(223,224)(227,228)(229,241)(230,242)(231,244)
(232,243)(233,245)(234,246)(235,248)(236,247)(237,249)(238,250)(239,252)
(240,251)(255,256)(259,260)(263,264)(265,277)(266,278)(267,280)(268,279)
(269,281)(270,282)(271,284)(272,283)(273,285)(274,286)(275,288)(276,287);;
s3 := ( 1,157)( 2,160)( 3,159)( 4,158)( 5,161)( 6,164)( 7,163)( 8,162)
( 9,165)( 10,168)( 11,167)( 12,166)( 13,145)( 14,148)( 15,147)( 16,146)
( 17,149)( 18,152)( 19,151)( 20,150)( 21,153)( 22,156)( 23,155)( 24,154)
( 25,169)( 26,172)( 27,171)( 28,170)( 29,173)( 30,176)( 31,175)( 32,174)
( 33,177)( 34,180)( 35,179)( 36,178)( 37,193)( 38,196)( 39,195)( 40,194)
( 41,197)( 42,200)( 43,199)( 44,198)( 45,201)( 46,204)( 47,203)( 48,202)
( 49,181)( 50,184)( 51,183)( 52,182)( 53,185)( 54,188)( 55,187)( 56,186)
( 57,189)( 58,192)( 59,191)( 60,190)( 61,205)( 62,208)( 63,207)( 64,206)
( 65,209)( 66,212)( 67,211)( 68,210)( 69,213)( 70,216)( 71,215)( 72,214)
( 73,229)( 74,232)( 75,231)( 76,230)( 77,233)( 78,236)( 79,235)( 80,234)
( 81,237)( 82,240)( 83,239)( 84,238)( 85,217)( 86,220)( 87,219)( 88,218)
( 89,221)( 90,224)( 91,223)( 92,222)( 93,225)( 94,228)( 95,227)( 96,226)
( 97,241)( 98,244)( 99,243)(100,242)(101,245)(102,248)(103,247)(104,246)
(105,249)(106,252)(107,251)(108,250)(109,265)(110,268)(111,267)(112,266)
(113,269)(114,272)(115,271)(116,270)(117,273)(118,276)(119,275)(120,274)
(121,253)(122,256)(123,255)(124,254)(125,257)(126,260)(127,259)(128,258)
(129,261)(130,264)(131,263)(132,262)(133,277)(134,280)(135,279)(136,278)
(137,281)(138,284)(139,283)(140,282)(141,285)(142,288)(143,287)(144,286);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)!( 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)( 73,109)( 74,110)( 75,111)( 76,112)( 77,117)( 78,118)( 79,119)
( 80,120)( 81,113)( 82,114)( 83,115)( 84,116)( 85,121)( 86,122)( 87,123)
( 88,124)( 89,129)( 90,130)( 91,131)( 92,132)( 93,125)( 94,126)( 95,127)
( 96,128)( 97,133)( 98,134)( 99,135)(100,136)(101,141)(102,142)(103,143)
(104,144)(105,137)(106,138)(107,139)(108,140)(149,153)(150,154)(151,155)
(152,156)(161,165)(162,166)(163,167)(164,168)(173,177)(174,178)(175,179)
(176,180)(185,189)(186,190)(187,191)(188,192)(197,201)(198,202)(199,203)
(200,204)(209,213)(210,214)(211,215)(212,216)(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, 79)( 2, 80)( 3, 77)( 4, 78)( 5, 75)( 6, 76)( 7, 73)
( 8, 74)( 9, 83)( 10, 84)( 11, 81)( 12, 82)( 13, 91)( 14, 92)( 15, 89)
( 16, 90)( 17, 87)( 18, 88)( 19, 85)( 20, 86)( 21, 95)( 22, 96)( 23, 93)
( 24, 94)( 25,103)( 26,104)( 27,101)( 28,102)( 29, 99)( 30,100)( 31, 97)
( 32, 98)( 33,107)( 34,108)( 35,105)( 36,106)( 37,115)( 38,116)( 39,113)
( 40,114)( 41,111)( 42,112)( 43,109)( 44,110)( 45,119)( 46,120)( 47,117)
( 48,118)( 49,127)( 50,128)( 51,125)( 52,126)( 53,123)( 54,124)( 55,121)
( 56,122)( 57,131)( 58,132)( 59,129)( 60,130)( 61,139)( 62,140)( 63,137)
( 64,138)( 65,135)( 66,136)( 67,133)( 68,134)( 69,143)( 70,144)( 71,141)
( 72,142)(145,223)(146,224)(147,221)(148,222)(149,219)(150,220)(151,217)
(152,218)(153,227)(154,228)(155,225)(156,226)(157,235)(158,236)(159,233)
(160,234)(161,231)(162,232)(163,229)(164,230)(165,239)(166,240)(167,237)
(168,238)(169,247)(170,248)(171,245)(172,246)(173,243)(174,244)(175,241)
(176,242)(177,251)(178,252)(179,249)(180,250)(181,259)(182,260)(183,257)
(184,258)(185,255)(186,256)(187,253)(188,254)(189,263)(190,264)(191,261)
(192,262)(193,271)(194,272)(195,269)(196,270)(197,267)(198,268)(199,265)
(200,266)(201,275)(202,276)(203,273)(204,274)(205,283)(206,284)(207,281)
(208,282)(209,279)(210,280)(211,277)(212,278)(213,287)(214,288)(215,285)
(216,286);
s2 := Sym(288)!( 3, 4)( 7, 8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)
( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)
( 39, 40)( 43, 44)( 47, 48)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 65)
( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 75, 76)
( 79, 80)( 83, 84)( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,101)( 90,102)
( 91,104)( 92,103)( 93,105)( 94,106)( 95,108)( 96,107)(111,112)(115,116)
(119,120)(121,133)(122,134)(123,136)(124,135)(125,137)(126,138)(127,140)
(128,139)(129,141)(130,142)(131,144)(132,143)(147,148)(151,152)(155,156)
(157,169)(158,170)(159,172)(160,171)(161,173)(162,174)(163,176)(164,175)
(165,177)(166,178)(167,180)(168,179)(183,184)(187,188)(191,192)(193,205)
(194,206)(195,208)(196,207)(197,209)(198,210)(199,212)(200,211)(201,213)
(202,214)(203,216)(204,215)(219,220)(223,224)(227,228)(229,241)(230,242)
(231,244)(232,243)(233,245)(234,246)(235,248)(236,247)(237,249)(238,250)
(239,252)(240,251)(255,256)(259,260)(263,264)(265,277)(266,278)(267,280)
(268,279)(269,281)(270,282)(271,284)(272,283)(273,285)(274,286)(275,288)
(276,287);
s3 := Sym(288)!( 1,157)( 2,160)( 3,159)( 4,158)( 5,161)( 6,164)( 7,163)
( 8,162)( 9,165)( 10,168)( 11,167)( 12,166)( 13,145)( 14,148)( 15,147)
( 16,146)( 17,149)( 18,152)( 19,151)( 20,150)( 21,153)( 22,156)( 23,155)
( 24,154)( 25,169)( 26,172)( 27,171)( 28,170)( 29,173)( 30,176)( 31,175)
( 32,174)( 33,177)( 34,180)( 35,179)( 36,178)( 37,193)( 38,196)( 39,195)
( 40,194)( 41,197)( 42,200)( 43,199)( 44,198)( 45,201)( 46,204)( 47,203)
( 48,202)( 49,181)( 50,184)( 51,183)( 52,182)( 53,185)( 54,188)( 55,187)
( 56,186)( 57,189)( 58,192)( 59,191)( 60,190)( 61,205)( 62,208)( 63,207)
( 64,206)( 65,209)( 66,212)( 67,211)( 68,210)( 69,213)( 70,216)( 71,215)
( 72,214)( 73,229)( 74,232)( 75,231)( 76,230)( 77,233)( 78,236)( 79,235)
( 80,234)( 81,237)( 82,240)( 83,239)( 84,238)( 85,217)( 86,220)( 87,219)
( 88,218)( 89,221)( 90,224)( 91,223)( 92,222)( 93,225)( 94,228)( 95,227)
( 96,226)( 97,241)( 98,244)( 99,243)(100,242)(101,245)(102,248)(103,247)
(104,246)(105,249)(106,252)(107,251)(108,250)(109,265)(110,268)(111,267)
(112,266)(113,269)(114,272)(115,271)(116,270)(117,273)(118,276)(119,275)
(120,274)(121,253)(122,256)(123,255)(124,254)(125,257)(126,260)(127,259)
(128,258)(129,261)(130,264)(131,263)(132,262)(133,277)(134,280)(135,279)
(136,278)(137,281)(138,284)(139,283)(140,282)(141,285)(142,288)(143,287)
(144,286);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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