Polytope of Type {24,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,3}*288
if this polytope has a name.
Group : SmallGroup(288,847)
Rank : 3
Schlafli Type : {24,3}
Number of vertices, edges, etc : 48, 72, 6
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 24
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {24,3,2} of size 576
   {24,3,4} of size 1152
   {24,3,6} of size 1728
Vertex Figure Of :
   {2,24,3} of size 576
   {4,24,3} of size 1152
   {6,24,3} of size 1728
   {6,24,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,3}*144
   3-fold quotients : {8,3}*96
   6-fold quotients : {4,3}*48
   8-fold quotients : {6,3}*36
   12-fold quotients : {4,3}*24
   24-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,6}*576b
   3-fold covers : {24,9}*864, {24,3}*864
   4-fold covers : {24,3}*1152a, {24,12}*1152l, {24,12}*1152m, {24,6}*1152l, {24,3}*1152b
   5-fold covers : {24,15}*1440
   6-fold covers : {24,18}*1728b, {24,6}*1728b, {24,6}*1728f
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope