Polytope of Type {6,24} with group SmallGroup(1152,155788)

Overview

Group: SmallGroup(1152,155788)
Rank: 3
Schläfli Type: {6,24}
Vertices, edges, …: 24, 288, 96
Order of s₀s₁s₂: 12
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

3-fold

{6,8}*384f

4-fold

{6,12}*288a

6-fold

8-fold

12-fold

16-fold

{6,6}*72a

24-fold

48-fold

72-fold

{2,4}*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*s1)^2> of order 3

48 facets

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

8 vertex figures

8 of {24}*48

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.