Polytope of Type {24,12} with group SmallGroup(1152,155788)

Overview

Group: SmallGroup(1152,155788)
Rank: 3
Schläfli Type: {24,12}
Vertices, edges, …: 48, 288, 24
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 24
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

{8,12}*384g

4-fold

{12,6}*288b

6-fold

8-fold

{12,3}*144

12-fold

{4,6}*96

16-fold

{6,6}*72b

24-fold

32-fold

{6,3}*36

48-fold

96-fold

{2,3}*12

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

12 facets

12 of {24}*48

24 vertex figures

24 of {12}*24

P/N, where N=<s1*s0*(s2*s1)^2*(s0*s1)^2*s2> of order 2

12 facets

12 of {24}*48

24 vertex figures

24 of {12}*24

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

References

None.

to this polytope.