Polytope of Type {6,4,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,12}*1152c
if this polytope has a name.
Group : SmallGroup(1152,157550)
Rank : 4
Schlafli Type : {6,4,12}
Number of vertices, edges, etc : 12, 24, 48, 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 : {3,4,12}*576, {6,4,6}*576b
3-fold quotients : {6,4,4}*384d
4-fold quotients : {6,2,12}*288, {3,4,6}*288
6-fold quotients : {3,4,4}*192b, {6,4,2}*192
8-fold quotients : {3,2,12}*144, {6,2,6}*144
12-fold quotients : {2,2,12}*96, {6,2,4}*96, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
16-fold quotients : {3,2,6}*72, {6,2,3}*72
24-fold quotients : {3,2,4}*48, {3,4,2}*48, {2,2,6}*48, {6,2,2}*48
32-fold quotients : {3,2,3}*36
36-fold quotients : {2,2,4}*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.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
12 facets:
12 of 2-fold non-regular quotient of {6,4}*96
8 vertex figures:
4 of {4,12}*96a
4 of {2,12}*48
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 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);;
s2 := ( 1, 2)( 3, 4)( 5, 10)( 6, 9)( 7, 12)( 8, 11)( 13, 14)( 15, 16)( 17, 22)( 18, 21)( 19, 24)( 20, 23)( 25, 26)( 27, 28)( 29, 34)( 30, 33)( 31, 36)( 32, 35)( 37, 38)( 39, 40)( 41, 46)( 42, 45)( 43, 48)( 44, 47)( 49, 50)( 51, 52)( 53, 58)( 54, 57)( 55, 60)( 56, 59)( 61, 62)( 63, 64)( 65, 70)( 66, 69)( 67, 72)( 68, 71)( 73,110)( 74,109)( 75,112)( 76,111)( 77,118)( 78,117)( 79,120)( 80,119)( 81,114)( 82,113)( 83,116)( 84,115)( 85,122)( 86,121)( 87,124)( 88,123)( 89,130)( 90,129)( 91,132)( 92,131)( 93,126)( 94,125)( 95,128)( 96,127)( 97,134)( 98,133)( 99,136)(100,135)(101,142)(102,141)(103,144)(104,143)(105,138)(106,137)(107,140)(108,139)(145,146)(147,148)(149,154)(150,153)(151,156)(152,155)(157,158)(159,160)(161,166)(162,165)(163,168)(164,167)(169,170)(171,172)(173,178)(174,177)(175,180)(176,179)(181,182)(183,184)(185,190)(186,189)(187,192)(188,191)(193,194)(195,196)(197,202)(198,201)(199,204)(200,203)(205,206)(207,208)(209,214)(210,213)(211,216)(212,215)(217,254)(218,253)(219,256)(220,255)(221,262)(222,261)(223,264)(224,263)(225,258)(226,257)(227,260)(228,259)(229,266)(230,265)(231,268)(232,267)(233,274)(234,273)(235,276)(236,275)(237,270)(238,269)(239,272)(240,271)(241,278)(242,277)(243,280)(244,279)(245,286)(246,285)(247,288)(248,287)(249,282)(250,281)(251,284)(252,283);;
s3 := ( 1, 77)( 2, 78)( 3, 79)( 4, 80)( 5, 73)( 6, 74)( 7, 75)( 8, 76)( 9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 89)( 14, 90)( 15, 91)( 16, 92)( 17, 85)( 18, 86)( 19, 87)( 20, 88)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25,101)( 26,102)( 27,103)( 28,104)( 29, 97)( 30, 98)( 31, 99)( 32,100)( 33,105)( 34,106)( 35,107)( 36,108)( 37,113)( 38,114)( 39,115)( 40,116)( 41,109)( 42,110)( 43,111)( 44,112)( 45,117)( 46,118)( 47,119)( 48,120)( 49,125)( 50,126)( 51,127)( 52,128)( 53,121)( 54,122)( 55,123)( 56,124)( 57,129)( 58,130)( 59,131)( 60,132)( 61,137)( 62,138)( 63,139)( 64,140)( 65,133)( 66,134)( 67,135)( 68,136)( 69,141)( 70,142)( 71,143)( 72,144)(145,221)(146,222)(147,223)(148,224)(149,217)(150,218)(151,219)(152,220)(153,225)(154,226)(155,227)(156,228)(157,233)(158,234)(159,235)(160,236)(161,229)(162,230)(163,231)(164,232)(165,237)(166,238)(167,239)(168,240)(169,245)(170,246)(171,247)(172,248)(173,241)(174,242)(175,243)(176,244)(177,249)(178,250)(179,251)(180,252)(181,257)(182,258)(183,259)(184,260)(185,253)(186,254)(187,255)(188,256)(189,261)(190,262)(191,263)(192,264)(193,269)(194,270)(195,271)(196,272)(197,265)(198,266)(199,267)(200,268)(201,273)(202,274)(203,275)(204,276)(205,281)(206,282)(207,283)(208,284)(209,277)(210,278)(211,279)(212,280)(213,285)(214,286)(215,287)(216,288);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := 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);
s2 := Sym(288)!( 1, 2)( 3, 4)( 5, 10)( 6, 9)( 7, 12)( 8, 11)( 13, 14)( 15, 16)( 17, 22)( 18, 21)( 19, 24)( 20, 23)( 25, 26)( 27, 28)( 29, 34)( 30, 33)( 31, 36)( 32, 35)( 37, 38)( 39, 40)( 41, 46)( 42, 45)( 43, 48)( 44, 47)( 49, 50)( 51, 52)( 53, 58)( 54, 57)( 55, 60)( 56, 59)( 61, 62)( 63, 64)( 65, 70)( 66, 69)( 67, 72)( 68, 71)( 73,110)( 74,109)( 75,112)( 76,111)( 77,118)( 78,117)( 79,120)( 80,119)( 81,114)( 82,113)( 83,116)( 84,115)( 85,122)( 86,121)( 87,124)( 88,123)( 89,130)( 90,129)( 91,132)( 92,131)( 93,126)( 94,125)( 95,128)( 96,127)( 97,134)( 98,133)( 99,136)(100,135)(101,142)(102,141)(103,144)(104,143)(105,138)(106,137)(107,140)(108,139)(145,146)(147,148)(149,154)(150,153)(151,156)(152,155)(157,158)(159,160)(161,166)(162,165)(163,168)(164,167)(169,170)(171,172)(173,178)(174,177)(175,180)(176,179)(181,182)(183,184)(185,190)(186,189)(187,192)(188,191)(193,194)(195,196)(197,202)(198,201)(199,204)(200,203)(205,206)(207,208)(209,214)(210,213)(211,216)(212,215)(217,254)(218,253)(219,256)(220,255)(221,262)(222,261)(223,264)(224,263)(225,258)(226,257)(227,260)(228,259)(229,266)(230,265)(231,268)(232,267)(233,274)(234,273)(235,276)(236,275)(237,270)(238,269)(239,272)(240,271)(241,278)(242,277)(243,280)(244,279)(245,286)(246,285)(247,288)(248,287)(249,282)(250,281)(251,284)(252,283);
s3 := Sym(288)!( 1, 77)( 2, 78)( 3, 79)( 4, 80)( 5, 73)( 6, 74)( 7, 75)( 8, 76)( 9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 89)( 14, 90)( 15, 91)( 16, 92)( 17, 85)( 18, 86)( 19, 87)( 20, 88)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25,101)( 26,102)( 27,103)( 28,104)( 29, 97)( 30, 98)( 31, 99)( 32,100)( 33,105)( 34,106)( 35,107)( 36,108)( 37,113)( 38,114)( 39,115)( 40,116)( 41,109)( 42,110)( 43,111)( 44,112)( 45,117)( 46,118)( 47,119)( 48,120)( 49,125)( 50,126)( 51,127)( 52,128)( 53,121)( 54,122)( 55,123)( 56,124)( 57,129)( 58,130)( 59,131)( 60,132)( 61,137)( 62,138)( 63,139)( 64,140)( 65,133)( 66,134)( 67,135)( 68,136)( 69,141)( 70,142)( 71,143)( 72,144)(145,221)(146,222)(147,223)(148,224)(149,217)(150,218)(151,219)(152,220)(153,225)(154,226)(155,227)(156,228)(157,233)(158,234)(159,235)(160,236)(161,229)(162,230)(163,231)(164,232)(165,237)(166,238)(167,239)(168,240)(169,245)(170,246)(171,247)(172,248)(173,241)(174,242)(175,243)(176,244)(177,249)(178,250)(179,251)(180,252)(181,257)(182,258)(183,259)(184,260)(185,253)(186,254)(187,255)(188,256)(189,261)(190,262)(191,263)(192,264)(193,269)(194,270)(195,271)(196,272)(197,265)(198,266)(199,267)(200,268)(201,273)(202,274)(203,275)(204,276)(205,281)(206,282)(207,283)(208,284)(209,277)(210,278)(211,279)(212,280)(213,285)(214,286)(215,287)(216,288);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope