Polytope of Type {4,12,6} with group SmallGroup(1152,157640)

Overview

Group: SmallGroup(1152,157640)
Rank: 4
Schläfli Type: {4,12,6}
Vertices, edges, …: 4, 48, 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

{4,4,6}*384d

4-fold

6-fold

8-fold

12-fold

16-fold

{2,6,3}*72

24-fold

36-fold

{4,2,2}*32

48-fold

{2,2,3}*24

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=<(s1*s2)^6> of order 2

8 facets

4 of {4,6}*48a
4 of {4,12}*96a

4 vertex figures

4 of 2-fold non-regular quotient of {12,6}*288b

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.