Polytope of Type {12,6} with group SmallGroup(1152,155849)

Overview

Group: SmallGroup(1152,155849)
Rank: 3
Schläfli Type: {12,6}
Vertices, edges, …: 96, 288, 48
Order of s₀s₁s₂: 24
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{12,6}*576b

3-fold

{4,6}*384b

4-fold

{12,6}*288a

6-fold

{4,6}*192b

8-fold

12-fold

{4,6}*96

16-fold

{6,6}*72a

24-fold

48-fold

72-fold

{4,2}*16

96-fold

144-fold

{2,2}*8

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*(s2*(s1*s0)^2)^2*s2*s1*s0*s1*s2> of order 2

28 facets

20 of {12}*24
8 of {6}*12

48 vertex figures

48 of {6}*12

P/N, where N=<(s1*s2)^2> of order 3

16 facets

16 of {12}*24

48 vertex figures

24 of {2}*4
24 of {6}*12

Representations

Permutation Representation (GAP)

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

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.