Polytope of Type {4,3,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157851)
Rank : 4
Schlafli Type : {4,3,6}
Number of vertices, edges, etc : 8, 48, 72, 24
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Locally Toroidal
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 : {4,3,6}*576
4-fold quotients : {4,3,6}*288, {2,3,6}*288
8-fold quotients : {4,3,6}*144
12-fold quotients : {2,3,6}*96, {4,3,2}*96
16-fold quotients : {2,3,6}*72
24-fold quotients : {2,3,3}*48, {4,3,2}*48
48-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s2*s1*s3*s2*s3*s2*s1*s3*s2*s3> of order 2.
12 facets:
12 of {4,3}*48
8 vertex figures:
8 of 2-fold non-regular quotient of {3,6}*144
P/N, where N=<s0*s1*s0*s1> of order 2.
24 facets:
24 of 2-fold non-regular quotient of {4,3}*48
4 vertex figures:
4 of {3,6}*144
P/N, where N=<s1*s3*s2*s1*s3*s2*s1*s3*s2*s3> of order 3.
8 facets:
8 of {4,3}*48
8 vertex figures:
8 of 3-fold non-regular quotient of {3,6}*144
P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s3*s2*s3*s2*s1*s3*s2> of order 4.
12 facets:
12 of 2-fold non-regular quotient of {4,3}*48
4 vertex figures:
4 of 2-fold non-regular quotient of {3,6}*144
P/N, where N=<s0*s1*s0*s1, s2*s1*s3*s2*s3*s2*s1*s3*s2*s3> of order 4.
12 facets:
12 of 2-fold non-regular quotient of {4,3}*48
4 vertex figures:
4 of 2-fold non-regular quotient of {3,6}*144
P/N, where N=<s1*s2*s3*s2*s1*s3*s2*s3*s2> of order 4.
6 facets:
6 of {4,3}*48
8 vertex figures:
8 of 4-fold non-regular quotient of {3,6}*144
P/N, where N=<s0*s1*s0*s1, s1*s3*s2*s1*s3*s2*s1*s3*s2*s3> of order 6.
8 facets:
8 of 2-fold non-regular quotient of {4,3}*48
4 vertex figures:
4 of 3-fold non-regular quotient of {3,6}*144
P/N, where N=<s0*s1*s0*s1, s1*s2*s3*s2*s1*s3*s2*s3*s2> of order 8.
6 facets:
6 of 2-fold non-regular quotient of {4,3}*48
4 vertex figures:
4 of 4-fold non-regular quotient of {3,6}*144
Permutation Representation (GAP) :
s0 := ( 1,153)( 2,154)( 3,155)( 4,156)( 5,157)( 6,158)( 7,159)( 8,160)( 9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)( 16,152)( 17,169)( 18,170)( 19,171)( 20,172)( 21,173)( 22,174)( 23,175)( 24,176)( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)( 32,168)( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)( 40,192)( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)( 48,184)( 49,201)( 50,202)( 51,203)( 52,204)( 53,205)( 54,206)( 55,207)( 56,208)( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)( 64,200)( 65,217)( 66,218)( 67,219)( 68,220)( 69,221)( 70,222)( 71,223)( 72,224)( 73,209)( 74,210)( 75,211)( 76,212)( 77,213)( 78,214)( 79,215)( 80,216)( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)( 88,240)( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)( 96,232)( 97,249)( 98,250)( 99,251)(100,252)(101,253)(102,254)(103,255)(104,256)(105,241)(106,242)(107,243)(108,244)(109,245)(110,246)(111,247)(112,248)(113,265)(114,266)(115,267)(116,268)(117,269)(118,270)(119,271)(120,272)(121,257)(122,258)(123,259)(124,260)(125,261)(126,262)(127,263)(128,264)(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)(136,288)(137,273)(138,274)(139,275)(140,276)(141,277)(142,278)(143,279)(144,280);;
s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,129)( 66,130)( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)( 72,135)( 73,141)( 74,142)( 75,144)( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,113)( 82,114)( 83,116)( 84,115)( 85,117)( 86,118)( 87,120)( 88,119)( 89,125)( 90,126)( 91,128)( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(193,241)(194,242)(195,244)(196,243)(197,245)(198,246)(199,248)(200,247)(201,253)(202,254)(203,256)(204,255)(205,249)(206,250)(207,252)(208,251)(209,273)(210,274)(211,276)(212,275)(213,277)(214,278)(215,280)(216,279)(217,285)(218,286)(219,288)(220,287)(221,281)(222,282)(223,284)(224,283)(225,257)(226,258)(227,260)(228,259)(229,261)(230,262)(231,264)(232,263)(233,269)(234,270)(235,272)(236,271)(237,265)(238,266)(239,268)(240,267);;
s2 := ( 1, 65)( 2, 68)( 3, 67)( 4, 66)( 5, 77)( 6, 80)( 7, 79)( 8, 78)( 9, 73)( 10, 76)( 11, 75)( 12, 74)( 13, 69)( 14, 72)( 15, 71)( 16, 70)( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 61)( 22, 64)( 23, 63)( 24, 62)( 25, 57)( 26, 60)( 27, 59)( 28, 58)( 29, 53)( 30, 56)( 31, 55)( 32, 54)( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37, 93)( 38, 96)( 39, 95)( 40, 94)( 41, 89)( 42, 92)( 43, 91)( 44, 90)( 45, 85)( 46, 88)( 47, 87)( 48, 86)( 97,113)( 98,116)( 99,115)(100,114)(101,125)(102,128)(103,127)(104,126)(105,121)(106,124)(107,123)(108,122)(109,117)(110,120)(111,119)(112,118)(130,132)(133,141)(134,144)(135,143)(136,142)(138,140)(145,209)(146,212)(147,211)(148,210)(149,221)(150,224)(151,223)(152,222)(153,217)(154,220)(155,219)(156,218)(157,213)(158,216)(159,215)(160,214)(161,193)(162,196)(163,195)(164,194)(165,205)(166,208)(167,207)(168,206)(169,201)(170,204)(171,203)(172,202)(173,197)(174,200)(175,199)(176,198)(177,225)(178,228)(179,227)(180,226)(181,237)(182,240)(183,239)(184,238)(185,233)(186,236)(187,235)(188,234)(189,229)(190,232)(191,231)(192,230)(241,257)(242,260)(243,259)(244,258)(245,269)(246,272)(247,271)(248,270)(249,265)(250,268)(251,267)(252,266)(253,261)(254,264)(255,263)(256,262)(274,276)(277,285)(278,288)(279,287)(280,286)(282,284);;
s3 := ( 1, 2)( 5, 6)( 9, 10)( 13, 14)( 17, 18)( 21, 22)( 25, 26)( 29, 30)( 33, 34)( 37, 38)( 41, 42)( 45, 46)( 49, 98)( 50, 97)( 51, 99)( 52,100)( 53,102)( 54,101)( 55,103)( 56,104)( 57,106)( 58,105)( 59,107)( 60,108)( 61,110)( 62,109)( 63,111)( 64,112)( 65,114)( 66,113)( 67,115)( 68,116)( 69,118)( 70,117)( 71,119)( 72,120)( 73,122)( 74,121)( 75,123)( 76,124)( 77,126)( 78,125)( 79,127)( 80,128)( 81,130)( 82,129)( 83,131)( 84,132)( 85,134)( 86,133)( 87,135)( 88,136)( 89,138)( 90,137)( 91,139)( 92,140)( 93,142)( 94,141)( 95,143)( 96,144)(145,146)(149,150)(153,154)(157,158)(161,162)(165,166)(169,170)(173,174)(177,178)(181,182)(185,186)(189,190)(193,242)(194,241)(195,243)(196,244)(197,246)(198,245)(199,247)(200,248)(201,250)(202,249)(203,251)(204,252)(205,254)(206,253)(207,255)(208,256)(209,258)(210,257)(211,259)(212,260)(213,262)(214,261)(215,263)(216,264)(217,266)(218,265)(219,267)(220,268)(221,270)(222,269)(223,271)(224,272)(225,274)(226,273)(227,275)(228,276)(229,278)(230,277)(231,279)(232,280)(233,282)(234,281)(235,283)(236,284)(237,286)(238,285)(239,287)(240,288);;
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,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 1,153)( 2,154)( 3,155)( 4,156)( 5,157)( 6,158)( 7,159)( 8,160)( 9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)( 16,152)( 17,169)( 18,170)( 19,171)( 20,172)( 21,173)( 22,174)( 23,175)( 24,176)( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)( 32,168)( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)( 40,192)( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)( 48,184)( 49,201)( 50,202)( 51,203)( 52,204)( 53,205)( 54,206)( 55,207)( 56,208)( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)( 64,200)( 65,217)( 66,218)( 67,219)( 68,220)( 69,221)( 70,222)( 71,223)( 72,224)( 73,209)( 74,210)( 75,211)( 76,212)( 77,213)( 78,214)( 79,215)( 80,216)( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)( 88,240)( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)( 96,232)( 97,249)( 98,250)( 99,251)(100,252)(101,253)(102,254)(103,255)(104,256)(105,241)(106,242)(107,243)(108,244)(109,245)(110,246)(111,247)(112,248)(113,265)(114,266)(115,267)(116,268)(117,269)(118,270)(119,271)(120,272)(121,257)(122,258)(123,259)(124,260)(125,261)(126,262)(127,263)(128,264)(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)(136,288)(137,273)(138,274)(139,275)(140,276)(141,277)(142,278)(143,279)(144,280);
s1 := Sym(288)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,129)( 66,130)( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)( 72,135)( 73,141)( 74,142)( 75,144)( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,113)( 82,114)( 83,116)( 84,115)( 85,117)( 86,118)( 87,120)( 88,119)( 89,125)( 90,126)( 91,128)( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(193,241)(194,242)(195,244)(196,243)(197,245)(198,246)(199,248)(200,247)(201,253)(202,254)(203,256)(204,255)(205,249)(206,250)(207,252)(208,251)(209,273)(210,274)(211,276)(212,275)(213,277)(214,278)(215,280)(216,279)(217,285)(218,286)(219,288)(220,287)(221,281)(222,282)(223,284)(224,283)(225,257)(226,258)(227,260)(228,259)(229,261)(230,262)(231,264)(232,263)(233,269)(234,270)(235,272)(236,271)(237,265)(238,266)(239,268)(240,267);
s2 := Sym(288)!( 1, 65)( 2, 68)( 3, 67)( 4, 66)( 5, 77)( 6, 80)( 7, 79)( 8, 78)( 9, 73)( 10, 76)( 11, 75)( 12, 74)( 13, 69)( 14, 72)( 15, 71)( 16, 70)( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 61)( 22, 64)( 23, 63)( 24, 62)( 25, 57)( 26, 60)( 27, 59)( 28, 58)( 29, 53)( 30, 56)( 31, 55)( 32, 54)( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37, 93)( 38, 96)( 39, 95)( 40, 94)( 41, 89)( 42, 92)( 43, 91)( 44, 90)( 45, 85)( 46, 88)( 47, 87)( 48, 86)( 97,113)( 98,116)( 99,115)(100,114)(101,125)(102,128)(103,127)(104,126)(105,121)(106,124)(107,123)(108,122)(109,117)(110,120)(111,119)(112,118)(130,132)(133,141)(134,144)(135,143)(136,142)(138,140)(145,209)(146,212)(147,211)(148,210)(149,221)(150,224)(151,223)(152,222)(153,217)(154,220)(155,219)(156,218)(157,213)(158,216)(159,215)(160,214)(161,193)(162,196)(163,195)(164,194)(165,205)(166,208)(167,207)(168,206)(169,201)(170,204)(171,203)(172,202)(173,197)(174,200)(175,199)(176,198)(177,225)(178,228)(179,227)(180,226)(181,237)(182,240)(183,239)(184,238)(185,233)(186,236)(187,235)(188,234)(189,229)(190,232)(191,231)(192,230)(241,257)(242,260)(243,259)(244,258)(245,269)(246,272)(247,271)(248,270)(249,265)(250,268)(251,267)(252,266)(253,261)(254,264)(255,263)(256,262)(274,276)(277,285)(278,288)(279,287)(280,286)(282,284);
s3 := Sym(288)!( 1, 2)( 5, 6)( 9, 10)( 13, 14)( 17, 18)( 21, 22)( 25, 26)( 29, 30)( 33, 34)( 37, 38)( 41, 42)( 45, 46)( 49, 98)( 50, 97)( 51, 99)( 52,100)( 53,102)( 54,101)( 55,103)( 56,104)( 57,106)( 58,105)( 59,107)( 60,108)( 61,110)( 62,109)( 63,111)( 64,112)( 65,114)( 66,113)( 67,115)( 68,116)( 69,118)( 70,117)( 71,119)( 72,120)( 73,122)( 74,121)( 75,123)( 76,124)( 77,126)( 78,125)( 79,127)( 80,128)( 81,130)( 82,129)( 83,131)( 84,132)( 85,134)( 86,133)( 87,135)( 88,136)( 89,138)( 90,137)( 91,139)( 92,140)( 93,142)( 94,141)( 95,143)( 96,144)(145,146)(149,150)(153,154)(157,158)(161,162)(165,166)(169,170)(173,174)(177,178)(181,182)(185,186)(189,190)(193,242)(194,241)(195,243)(196,244)(197,246)(198,245)(199,247)(200,248)(201,250)(202,249)(203,251)(204,252)(205,254)(206,253)(207,255)(208,256)(209,258)(210,257)(211,259)(212,260)(213,262)(214,261)(215,263)(216,264)(217,266)(218,265)(219,267)(220,268)(221,270)(222,269)(223,271)(224,272)(225,274)(226,273)(227,275)(228,276)(229,278)(230,277)(231,279)(232,280)(233,282)(234,281)(235,283)(236,284)(237,286)(238,285)(239,287)(240,288);
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;
References : None.
to this polytope