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