Polytope of Type {4,6,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,12}*1152d
if this polytope has a name.
Group : SmallGroup(1152,157640)
Rank : 4
Schlafli Type : {4,6,12}
Number of vertices, edges, etc : 8, 24, 72, 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 : {4,6,12}*576e, {4,6,6}*576b
3-fold quotients : {4,6,4}*384b
4-fold quotients : {2,6,12}*288c, {4,3,6}*288, {4,6,6}*288e, {4,6,6}*288f
6-fold quotients : {4,6,4}*192c, {4,6,2}*192
8-fold quotients : {4,3,6}*144, {2,6,6}*144c
12-fold quotients : {2,6,4}*96a, {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
16-fold quotients : {2,3,6}*72
24-fold quotients : {4,3,2}*48, {2,6,2}*48
36-fold quotients : {2,2,4}*32
48-fold quotients : {2,3,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,147)( 2,148)( 3,145)( 4,146)( 5,151)( 6,152)( 7,149)( 8,150)
( 9,155)( 10,156)( 11,153)( 12,154)( 13,159)( 14,160)( 15,157)( 16,158)
( 17,163)( 18,164)( 19,161)( 20,162)( 21,167)( 22,168)( 23,165)( 24,166)
( 25,171)( 26,172)( 27,169)( 28,170)( 29,175)( 30,176)( 31,173)( 32,174)
( 33,179)( 34,180)( 35,177)( 36,178)( 37,183)( 38,184)( 39,181)( 40,182)
( 41,187)( 42,188)( 43,185)( 44,186)( 45,191)( 46,192)( 47,189)( 48,190)
( 49,195)( 50,196)( 51,193)( 52,194)( 53,199)( 54,200)( 55,197)( 56,198)
( 57,203)( 58,204)( 59,201)( 60,202)( 61,207)( 62,208)( 63,205)( 64,206)
( 65,211)( 66,212)( 67,209)( 68,210)( 69,215)( 70,216)( 71,213)( 72,214)
( 73,219)( 74,220)( 75,217)( 76,218)( 77,223)( 78,224)( 79,221)( 80,222)
( 81,227)( 82,228)( 83,225)( 84,226)( 85,231)( 86,232)( 87,229)( 88,230)
( 89,235)( 90,236)( 91,233)( 92,234)( 93,239)( 94,240)( 95,237)( 96,238)
( 97,243)( 98,244)( 99,241)(100,242)(101,247)(102,248)(103,245)(104,246)
(105,251)(106,252)(107,249)(108,250)(109,255)(110,256)(111,253)(112,254)
(113,259)(114,260)(115,257)(116,258)(117,263)(118,264)(119,261)(120,262)
(121,267)(122,268)(123,265)(124,266)(125,271)(126,272)(127,269)(128,270)
(129,275)(130,276)(131,273)(132,274)(133,279)(134,280)(135,277)(136,278)
(137,283)(138,284)(139,281)(140,282)(141,287)(142,288)(143,285)(144,286);;
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)(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);;
s2 := ( 1, 89)( 2, 92)( 3, 91)( 4, 90)( 5, 85)( 6, 88)( 7, 87)( 8, 86)
( 9, 93)( 10, 96)( 11, 95)( 12, 94)( 13, 77)( 14, 80)( 15, 79)( 16, 78)
( 17, 73)( 18, 76)( 19, 75)( 20, 74)( 21, 81)( 22, 84)( 23, 83)( 24, 82)
( 25,101)( 26,104)( 27,103)( 28,102)( 29, 97)( 30,100)( 31, 99)( 32, 98)
( 33,105)( 34,108)( 35,107)( 36,106)( 37,125)( 38,128)( 39,127)( 40,126)
( 41,121)( 42,124)( 43,123)( 44,122)( 45,129)( 46,132)( 47,131)( 48,130)
( 49,113)( 50,116)( 51,115)( 52,114)( 53,109)( 54,112)( 55,111)( 56,110)
( 57,117)( 58,120)( 59,119)( 60,118)( 61,137)( 62,140)( 63,139)( 64,138)
( 65,133)( 66,136)( 67,135)( 68,134)( 69,141)( 70,144)( 71,143)( 72,142)
(145,233)(146,236)(147,235)(148,234)(149,229)(150,232)(151,231)(152,230)
(153,237)(154,240)(155,239)(156,238)(157,221)(158,224)(159,223)(160,222)
(161,217)(162,220)(163,219)(164,218)(165,225)(166,228)(167,227)(168,226)
(169,245)(170,248)(171,247)(172,246)(173,241)(174,244)(175,243)(176,242)
(177,249)(178,252)(179,251)(180,250)(181,269)(182,272)(183,271)(184,270)
(185,265)(186,268)(187,267)(188,266)(189,273)(190,276)(191,275)(192,274)
(193,257)(194,260)(195,259)(196,258)(197,253)(198,256)(199,255)(200,254)
(201,261)(202,264)(203,263)(204,262)(205,281)(206,284)(207,283)(208,282)
(209,277)(210,280)(211,279)(212,278)(213,285)(214,288)(215,287)(216,286);;
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)
( 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);;
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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 1,147)( 2,148)( 3,145)( 4,146)( 5,151)( 6,152)( 7,149)
( 8,150)( 9,155)( 10,156)( 11,153)( 12,154)( 13,159)( 14,160)( 15,157)
( 16,158)( 17,163)( 18,164)( 19,161)( 20,162)( 21,167)( 22,168)( 23,165)
( 24,166)( 25,171)( 26,172)( 27,169)( 28,170)( 29,175)( 30,176)( 31,173)
( 32,174)( 33,179)( 34,180)( 35,177)( 36,178)( 37,183)( 38,184)( 39,181)
( 40,182)( 41,187)( 42,188)( 43,185)( 44,186)( 45,191)( 46,192)( 47,189)
( 48,190)( 49,195)( 50,196)( 51,193)( 52,194)( 53,199)( 54,200)( 55,197)
( 56,198)( 57,203)( 58,204)( 59,201)( 60,202)( 61,207)( 62,208)( 63,205)
( 64,206)( 65,211)( 66,212)( 67,209)( 68,210)( 69,215)( 70,216)( 71,213)
( 72,214)( 73,219)( 74,220)( 75,217)( 76,218)( 77,223)( 78,224)( 79,221)
( 80,222)( 81,227)( 82,228)( 83,225)( 84,226)( 85,231)( 86,232)( 87,229)
( 88,230)( 89,235)( 90,236)( 91,233)( 92,234)( 93,239)( 94,240)( 95,237)
( 96,238)( 97,243)( 98,244)( 99,241)(100,242)(101,247)(102,248)(103,245)
(104,246)(105,251)(106,252)(107,249)(108,250)(109,255)(110,256)(111,253)
(112,254)(113,259)(114,260)(115,257)(116,258)(117,263)(118,264)(119,261)
(120,262)(121,267)(122,268)(123,265)(124,266)(125,271)(126,272)(127,269)
(128,270)(129,275)(130,276)(131,273)(132,274)(133,279)(134,280)(135,277)
(136,278)(137,283)(138,284)(139,281)(140,282)(141,287)(142,288)(143,285)
(144,286);
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)(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);
s2 := Sym(288)!( 1, 89)( 2, 92)( 3, 91)( 4, 90)( 5, 85)( 6, 88)( 7, 87)
( 8, 86)( 9, 93)( 10, 96)( 11, 95)( 12, 94)( 13, 77)( 14, 80)( 15, 79)
( 16, 78)( 17, 73)( 18, 76)( 19, 75)( 20, 74)( 21, 81)( 22, 84)( 23, 83)
( 24, 82)( 25,101)( 26,104)( 27,103)( 28,102)( 29, 97)( 30,100)( 31, 99)
( 32, 98)( 33,105)( 34,108)( 35,107)( 36,106)( 37,125)( 38,128)( 39,127)
( 40,126)( 41,121)( 42,124)( 43,123)( 44,122)( 45,129)( 46,132)( 47,131)
( 48,130)( 49,113)( 50,116)( 51,115)( 52,114)( 53,109)( 54,112)( 55,111)
( 56,110)( 57,117)( 58,120)( 59,119)( 60,118)( 61,137)( 62,140)( 63,139)
( 64,138)( 65,133)( 66,136)( 67,135)( 68,134)( 69,141)( 70,144)( 71,143)
( 72,142)(145,233)(146,236)(147,235)(148,234)(149,229)(150,232)(151,231)
(152,230)(153,237)(154,240)(155,239)(156,238)(157,221)(158,224)(159,223)
(160,222)(161,217)(162,220)(163,219)(164,218)(165,225)(166,228)(167,227)
(168,226)(169,245)(170,248)(171,247)(172,246)(173,241)(174,244)(175,243)
(176,242)(177,249)(178,252)(179,251)(180,250)(181,269)(182,272)(183,271)
(184,270)(185,265)(186,268)(187,267)(188,266)(189,273)(190,276)(191,275)
(192,274)(193,257)(194,260)(195,259)(196,258)(197,253)(198,256)(199,255)
(200,254)(201,261)(202,264)(203,263)(204,262)(205,281)(206,284)(207,283)
(208,282)(209,277)(210,280)(211,279)(212,278)(213,285)(214,288)(215,287)
(216,286);
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)( 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);
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope