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Polytope of Type {2,3,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,24}*576
if this polytope has a name.
Group : SmallGroup(576,8319)
Rank : 4
Schlafli Type : {2,3,24}
Number of vertices, edges, etc : 2, 6, 72, 48
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,24,2} of size 1152
Vertex Figure Of :
   {2,2,3,24} of size 1152
   {3,2,3,24} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,12}*288
   3-fold quotients : {2,3,8}*192
   6-fold quotients : {2,3,4}*96
   8-fold quotients : {2,3,6}*72
   12-fold quotients : {2,3,4}*48
   24-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,24}*1152b
   3-fold covers : {2,9,24}*1728, {2,3,24}*1728, {6,3,24}*1728
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3,219)(  4,220)(  5,223)(  6,224)(  7,221)(  8,222)(  9,226)( 10,225)
( 11,235)( 12,236)( 13,239)( 14,240)( 15,237)( 16,238)( 17,242)( 18,241)
( 19,227)( 20,228)( 21,231)( 22,232)( 23,229)( 24,230)( 25,234)( 26,233)
( 27,267)( 28,268)( 29,271)( 30,272)( 31,269)( 32,270)( 33,274)( 34,273)
( 35,283)( 36,284)( 37,287)( 38,288)( 39,285)( 40,286)( 41,290)( 42,289)
( 43,275)( 44,276)( 45,279)( 46,280)( 47,277)( 48,278)( 49,282)( 50,281)
( 51,243)( 52,244)( 53,247)( 54,248)( 55,245)( 56,246)( 57,250)( 58,249)
( 59,259)( 60,260)( 61,263)( 62,264)( 63,261)( 64,262)( 65,266)( 66,265)
( 67,251)( 68,252)( 69,255)( 70,256)( 71,253)( 72,254)( 73,258)( 74,257)
( 75,148)( 76,147)( 77,152)( 78,151)( 79,150)( 80,149)( 81,153)( 82,154)
( 83,164)( 84,163)( 85,168)( 86,167)( 87,166)( 88,165)( 89,169)( 90,170)
( 91,156)( 92,155)( 93,160)( 94,159)( 95,158)( 96,157)( 97,161)( 98,162)
( 99,196)(100,195)(101,200)(102,199)(103,198)(104,197)(105,201)(106,202)
(107,212)(108,211)(109,216)(110,215)(111,214)(112,213)(113,217)(114,218)
(115,204)(116,203)(117,208)(118,207)(119,206)(120,205)(121,209)(122,210)
(123,172)(124,171)(125,176)(126,175)(127,174)(128,173)(129,177)(130,178)
(131,188)(132,187)(133,192)(134,191)(135,190)(136,189)(137,193)(138,194)
(139,180)(140,179)(141,184)(142,183)(143,182)(144,181)(145,185)(146,186);;
s2 := (  3,251)(  4,252)(  5,254)(  6,253)(  7,257)(  8,258)(  9,255)( 10,256)
( 11,243)( 12,244)( 13,246)( 14,245)( 15,249)( 16,250)( 17,247)( 18,248)
( 19,259)( 20,260)( 21,262)( 22,261)( 23,265)( 24,266)( 25,263)( 26,264)
( 27,227)( 28,228)( 29,230)( 30,229)( 31,233)( 32,234)( 33,231)( 34,232)
( 35,219)( 36,220)( 37,222)( 38,221)( 39,225)( 40,226)( 41,223)( 42,224)
( 43,235)( 44,236)( 45,238)( 46,237)( 47,241)( 48,242)( 49,239)( 50,240)
( 51,275)( 52,276)( 53,278)( 54,277)( 55,281)( 56,282)( 57,279)( 58,280)
( 59,267)( 60,268)( 61,270)( 62,269)( 63,273)( 64,274)( 65,271)( 66,272)
( 67,283)( 68,284)( 69,286)( 70,285)( 71,289)( 72,290)( 73,287)( 74,288)
( 75,180)( 76,179)( 77,181)( 78,182)( 79,186)( 80,185)( 81,184)( 82,183)
( 83,172)( 84,171)( 85,173)( 86,174)( 87,178)( 88,177)( 89,176)( 90,175)
( 91,188)( 92,187)( 93,189)( 94,190)( 95,194)( 96,193)( 97,192)( 98,191)
( 99,156)(100,155)(101,157)(102,158)(103,162)(104,161)(105,160)(106,159)
(107,148)(108,147)(109,149)(110,150)(111,154)(112,153)(113,152)(114,151)
(115,164)(116,163)(117,165)(118,166)(119,170)(120,169)(121,168)(122,167)
(123,204)(124,203)(125,205)(126,206)(127,210)(128,209)(129,208)(130,207)
(131,196)(132,195)(133,197)(134,198)(135,202)(136,201)(137,200)(138,199)
(139,212)(140,211)(141,213)(142,214)(143,218)(144,217)(145,216)(146,215);;
s3 := (  3,153)(  4,154)(  5,151)(  6,152)(  7,150)(  8,149)(  9,148)( 10,147)
( 11,169)( 12,170)( 13,167)( 14,168)( 15,166)( 16,165)( 17,164)( 18,163)
( 19,161)( 20,162)( 21,159)( 22,160)( 23,158)( 24,157)( 25,156)( 26,155)
( 27,177)( 28,178)( 29,175)( 30,176)( 31,174)( 32,173)( 33,172)( 34,171)
( 35,193)( 36,194)( 37,191)( 38,192)( 39,190)( 40,189)( 41,188)( 42,187)
( 43,185)( 44,186)( 45,183)( 46,184)( 47,182)( 48,181)( 49,180)( 50,179)
( 51,201)( 52,202)( 53,199)( 54,200)( 55,198)( 56,197)( 57,196)( 58,195)
( 59,217)( 60,218)( 61,215)( 62,216)( 63,214)( 64,213)( 65,212)( 66,211)
( 67,209)( 68,210)( 69,207)( 70,208)( 71,206)( 72,205)( 73,204)( 74,203)
( 75,226)( 76,225)( 77,224)( 78,223)( 79,221)( 80,222)( 81,219)( 82,220)
( 83,242)( 84,241)( 85,240)( 86,239)( 87,237)( 88,238)( 89,235)( 90,236)
( 91,234)( 92,233)( 93,232)( 94,231)( 95,229)( 96,230)( 97,227)( 98,228)
( 99,250)(100,249)(101,248)(102,247)(103,245)(104,246)(105,243)(106,244)
(107,266)(108,265)(109,264)(110,263)(111,261)(112,262)(113,259)(114,260)
(115,258)(116,257)(117,256)(118,255)(119,253)(120,254)(121,251)(122,252)
(123,274)(124,273)(125,272)(126,271)(127,269)(128,270)(129,267)(130,268)
(131,290)(132,289)(133,288)(134,287)(135,285)(136,286)(137,283)(138,284)
(139,282)(140,281)(141,280)(142,279)(143,277)(144,278)(145,275)(146,276);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(290)!(1,2);
s1 := Sym(290)!(  3,219)(  4,220)(  5,223)(  6,224)(  7,221)(  8,222)(  9,226)
( 10,225)( 11,235)( 12,236)( 13,239)( 14,240)( 15,237)( 16,238)( 17,242)
( 18,241)( 19,227)( 20,228)( 21,231)( 22,232)( 23,229)( 24,230)( 25,234)
( 26,233)( 27,267)( 28,268)( 29,271)( 30,272)( 31,269)( 32,270)( 33,274)
( 34,273)( 35,283)( 36,284)( 37,287)( 38,288)( 39,285)( 40,286)( 41,290)
( 42,289)( 43,275)( 44,276)( 45,279)( 46,280)( 47,277)( 48,278)( 49,282)
( 50,281)( 51,243)( 52,244)( 53,247)( 54,248)( 55,245)( 56,246)( 57,250)
( 58,249)( 59,259)( 60,260)( 61,263)( 62,264)( 63,261)( 64,262)( 65,266)
( 66,265)( 67,251)( 68,252)( 69,255)( 70,256)( 71,253)( 72,254)( 73,258)
( 74,257)( 75,148)( 76,147)( 77,152)( 78,151)( 79,150)( 80,149)( 81,153)
( 82,154)( 83,164)( 84,163)( 85,168)( 86,167)( 87,166)( 88,165)( 89,169)
( 90,170)( 91,156)( 92,155)( 93,160)( 94,159)( 95,158)( 96,157)( 97,161)
( 98,162)( 99,196)(100,195)(101,200)(102,199)(103,198)(104,197)(105,201)
(106,202)(107,212)(108,211)(109,216)(110,215)(111,214)(112,213)(113,217)
(114,218)(115,204)(116,203)(117,208)(118,207)(119,206)(120,205)(121,209)
(122,210)(123,172)(124,171)(125,176)(126,175)(127,174)(128,173)(129,177)
(130,178)(131,188)(132,187)(133,192)(134,191)(135,190)(136,189)(137,193)
(138,194)(139,180)(140,179)(141,184)(142,183)(143,182)(144,181)(145,185)
(146,186);
s2 := Sym(290)!(  3,251)(  4,252)(  5,254)(  6,253)(  7,257)(  8,258)(  9,255)
( 10,256)( 11,243)( 12,244)( 13,246)( 14,245)( 15,249)( 16,250)( 17,247)
( 18,248)( 19,259)( 20,260)( 21,262)( 22,261)( 23,265)( 24,266)( 25,263)
( 26,264)( 27,227)( 28,228)( 29,230)( 30,229)( 31,233)( 32,234)( 33,231)
( 34,232)( 35,219)( 36,220)( 37,222)( 38,221)( 39,225)( 40,226)( 41,223)
( 42,224)( 43,235)( 44,236)( 45,238)( 46,237)( 47,241)( 48,242)( 49,239)
( 50,240)( 51,275)( 52,276)( 53,278)( 54,277)( 55,281)( 56,282)( 57,279)
( 58,280)( 59,267)( 60,268)( 61,270)( 62,269)( 63,273)( 64,274)( 65,271)
( 66,272)( 67,283)( 68,284)( 69,286)( 70,285)( 71,289)( 72,290)( 73,287)
( 74,288)( 75,180)( 76,179)( 77,181)( 78,182)( 79,186)( 80,185)( 81,184)
( 82,183)( 83,172)( 84,171)( 85,173)( 86,174)( 87,178)( 88,177)( 89,176)
( 90,175)( 91,188)( 92,187)( 93,189)( 94,190)( 95,194)( 96,193)( 97,192)
( 98,191)( 99,156)(100,155)(101,157)(102,158)(103,162)(104,161)(105,160)
(106,159)(107,148)(108,147)(109,149)(110,150)(111,154)(112,153)(113,152)
(114,151)(115,164)(116,163)(117,165)(118,166)(119,170)(120,169)(121,168)
(122,167)(123,204)(124,203)(125,205)(126,206)(127,210)(128,209)(129,208)
(130,207)(131,196)(132,195)(133,197)(134,198)(135,202)(136,201)(137,200)
(138,199)(139,212)(140,211)(141,213)(142,214)(143,218)(144,217)(145,216)
(146,215);
s3 := Sym(290)!(  3,153)(  4,154)(  5,151)(  6,152)(  7,150)(  8,149)(  9,148)
( 10,147)( 11,169)( 12,170)( 13,167)( 14,168)( 15,166)( 16,165)( 17,164)
( 18,163)( 19,161)( 20,162)( 21,159)( 22,160)( 23,158)( 24,157)( 25,156)
( 26,155)( 27,177)( 28,178)( 29,175)( 30,176)( 31,174)( 32,173)( 33,172)
( 34,171)( 35,193)( 36,194)( 37,191)( 38,192)( 39,190)( 40,189)( 41,188)
( 42,187)( 43,185)( 44,186)( 45,183)( 46,184)( 47,182)( 48,181)( 49,180)
( 50,179)( 51,201)( 52,202)( 53,199)( 54,200)( 55,198)( 56,197)( 57,196)
( 58,195)( 59,217)( 60,218)( 61,215)( 62,216)( 63,214)( 64,213)( 65,212)
( 66,211)( 67,209)( 68,210)( 69,207)( 70,208)( 71,206)( 72,205)( 73,204)
( 74,203)( 75,226)( 76,225)( 77,224)( 78,223)( 79,221)( 80,222)( 81,219)
( 82,220)( 83,242)( 84,241)( 85,240)( 86,239)( 87,237)( 88,238)( 89,235)
( 90,236)( 91,234)( 92,233)( 93,232)( 94,231)( 95,229)( 96,230)( 97,227)
( 98,228)( 99,250)(100,249)(101,248)(102,247)(103,245)(104,246)(105,243)
(106,244)(107,266)(108,265)(109,264)(110,263)(111,261)(112,262)(113,259)
(114,260)(115,258)(116,257)(117,256)(118,255)(119,253)(120,254)(121,251)
(122,252)(123,274)(124,273)(125,272)(126,271)(127,269)(128,270)(129,267)
(130,268)(131,290)(132,289)(133,288)(134,287)(135,285)(136,286)(137,283)
(138,284)(139,282)(140,281)(141,280)(142,279)(143,277)(144,278)(145,275)
(146,276);
poly := sub<Sym(290)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >; 
 

to this polytope