Polytope of Type {4,6,12} with group SmallGroup(1152,157550)

Overview

Group: SmallGroup(1152,157550)
Rank: 4
Schläfli Type: {4,6,12}
Vertices, edges, …: 8, 24, 72, 12
Order of s₀s₁s₂s₃: 12
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

3-fold

{4,6,4}*384b

4-fold

6-fold

8-fold

{2,6,6}*144a

12-fold

24-fold

36-fold

{2,2,4}*32

48-fold

72-fold

{2,2,2}*16

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^2> of order 2

12 facets

12 of 2-fold non-regular quotient of {4,6}*96

4 vertex figures

4 of {6,12}*144a

Representations

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