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

Overview

Group: SmallGroup(1152,157550)
Rank: 4
Schläfli Type: {6,6,12}
Vertices, edges, …: 8, 24, 48, 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

{6,6,4}*384

4-fold

{3,6,6}*288

6-fold

12-fold

24-fold

36-fold

{2,2,4}*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

None.

Representations

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