Polytope of Type {3,2,24,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,24,3}*1728
if this polytope has a name.
Group : SmallGroup(1728,46303)
Rank : 5
Schlafli Type : {3,2,24,3}
Number of vertices, edges, etc : 3, 3, 48, 72, 6
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,12,3}*864
3-fold quotients : {3,2,8,3}*576
6-fold quotients : {3,2,4,3}*288
8-fold quotients : {3,2,6,3}*216
12-fold quotients : {3,2,4,3}*144
24-fold quotients : {3,2,2,3}*72
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4,150)( 5,151)( 6,149)( 7,148)( 8,154)( 9,155)( 10,153)( 11,152)
( 12,166)( 13,167)( 14,165)( 15,164)( 16,170)( 17,171)( 18,169)( 19,168)
( 20,158)( 21,159)( 22,157)( 23,156)( 24,162)( 25,163)( 26,161)( 27,160)
( 28,174)( 29,175)( 30,173)( 31,172)( 32,178)( 33,179)( 34,177)( 35,176)
( 36,190)( 37,191)( 38,189)( 39,188)( 40,194)( 41,195)( 42,193)( 43,192)
( 44,182)( 45,183)( 46,181)( 47,180)( 48,186)( 49,187)( 50,185)( 51,184)
( 52,198)( 53,199)( 54,197)( 55,196)( 56,202)( 57,203)( 58,201)( 59,200)
( 60,214)( 61,215)( 62,213)( 63,212)( 64,218)( 65,219)( 66,217)( 67,216)
( 68,206)( 69,207)( 70,205)( 71,204)( 72,210)( 73,211)( 74,209)( 75,208)
( 76,223)( 77,222)( 78,220)( 79,221)( 80,227)( 81,226)( 82,224)( 83,225)
( 84,239)( 85,238)( 86,236)( 87,237)( 88,243)( 89,242)( 90,240)( 91,241)
( 92,231)( 93,230)( 94,228)( 95,229)( 96,235)( 97,234)( 98,232)( 99,233)
(100,247)(101,246)(102,244)(103,245)(104,251)(105,250)(106,248)(107,249)
(108,263)(109,262)(110,260)(111,261)(112,267)(113,266)(114,264)(115,265)
(116,255)(117,254)(118,252)(119,253)(120,259)(121,258)(122,256)(123,257)
(124,271)(125,270)(126,268)(127,269)(128,275)(129,274)(130,272)(131,273)
(132,287)(133,286)(134,284)(135,285)(136,291)(137,290)(138,288)(139,289)
(140,279)(141,278)(142,276)(143,277)(144,283)(145,282)(146,280)(147,281);;
s3 := ( 4,228)( 5,229)( 6,232)( 7,233)( 8,230)( 9,231)( 10,235)( 11,234)
( 12,220)( 13,221)( 14,224)( 15,225)( 16,222)( 17,223)( 18,227)( 19,226)
( 20,236)( 21,237)( 22,240)( 23,241)( 24,238)( 25,239)( 26,243)( 27,242)
( 28,276)( 29,277)( 30,280)( 31,281)( 32,278)( 33,279)( 34,283)( 35,282)
( 36,268)( 37,269)( 38,272)( 39,273)( 40,270)( 41,271)( 42,275)( 43,274)
( 44,284)( 45,285)( 46,288)( 47,289)( 48,286)( 49,287)( 50,291)( 51,290)
( 52,252)( 53,253)( 54,256)( 55,257)( 56,254)( 57,255)( 58,259)( 59,258)
( 60,244)( 61,245)( 62,248)( 63,249)( 64,246)( 65,247)( 66,251)( 67,250)
( 68,260)( 69,261)( 70,264)( 71,265)( 72,262)( 73,263)( 74,267)( 75,266)
( 76,157)( 77,156)( 78,161)( 79,160)( 80,159)( 81,158)( 82,162)( 83,163)
( 84,149)( 85,148)( 86,153)( 87,152)( 88,151)( 89,150)( 90,154)( 91,155)
( 92,165)( 93,164)( 94,169)( 95,168)( 96,167)( 97,166)( 98,170)( 99,171)
(100,205)(101,204)(102,209)(103,208)(104,207)(105,206)(106,210)(107,211)
(108,197)(109,196)(110,201)(111,200)(112,199)(113,198)(114,202)(115,203)
(116,213)(117,212)(118,217)(119,216)(120,215)(121,214)(122,218)(123,219)
(124,181)(125,180)(126,185)(127,184)(128,183)(129,182)(130,186)(131,187)
(132,173)(133,172)(134,177)(135,176)(136,175)(137,174)(138,178)(139,179)
(140,189)(141,188)(142,193)(143,192)(144,191)(145,190)(146,194)(147,195);;
s4 := ( 4,244)( 5,245)( 6,247)( 7,246)( 8,250)( 9,251)( 10,248)( 11,249)
( 12,260)( 13,261)( 14,263)( 15,262)( 16,266)( 17,267)( 18,264)( 19,265)
( 20,252)( 21,253)( 22,255)( 23,254)( 24,258)( 25,259)( 26,256)( 27,257)
( 28,220)( 29,221)( 30,223)( 31,222)( 32,226)( 33,227)( 34,224)( 35,225)
( 36,236)( 37,237)( 38,239)( 39,238)( 40,242)( 41,243)( 42,240)( 43,241)
( 44,228)( 45,229)( 46,231)( 47,230)( 48,234)( 49,235)( 50,232)( 51,233)
( 52,268)( 53,269)( 54,271)( 55,270)( 56,274)( 57,275)( 58,272)( 59,273)
( 60,284)( 61,285)( 62,287)( 63,286)( 64,290)( 65,291)( 66,288)( 67,289)
( 68,276)( 69,277)( 70,279)( 71,278)( 72,282)( 73,283)( 74,280)( 75,281)
( 76,173)( 77,172)( 78,174)( 79,175)( 80,179)( 81,178)( 82,177)( 83,176)
( 84,189)( 85,188)( 86,190)( 87,191)( 88,195)( 89,194)( 90,193)( 91,192)
( 92,181)( 93,180)( 94,182)( 95,183)( 96,187)( 97,186)( 98,185)( 99,184)
(100,149)(101,148)(102,150)(103,151)(104,155)(105,154)(106,153)(107,152)
(108,165)(109,164)(110,166)(111,167)(112,171)(113,170)(114,169)(115,168)
(116,157)(117,156)(118,158)(119,159)(120,163)(121,162)(122,161)(123,160)
(124,197)(125,196)(126,198)(127,199)(128,203)(129,202)(130,201)(131,200)
(132,213)(133,212)(134,214)(135,215)(136,219)(137,218)(138,217)(139,216)
(140,205)(141,204)(142,206)(143,207)(144,211)(145,210)(146,209)(147,208);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4,
s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(291)!(2,3);
s1 := Sym(291)!(1,2);
s2 := Sym(291)!( 4,150)( 5,151)( 6,149)( 7,148)( 8,154)( 9,155)( 10,153)
( 11,152)( 12,166)( 13,167)( 14,165)( 15,164)( 16,170)( 17,171)( 18,169)
( 19,168)( 20,158)( 21,159)( 22,157)( 23,156)( 24,162)( 25,163)( 26,161)
( 27,160)( 28,174)( 29,175)( 30,173)( 31,172)( 32,178)( 33,179)( 34,177)
( 35,176)( 36,190)( 37,191)( 38,189)( 39,188)( 40,194)( 41,195)( 42,193)
( 43,192)( 44,182)( 45,183)( 46,181)( 47,180)( 48,186)( 49,187)( 50,185)
( 51,184)( 52,198)( 53,199)( 54,197)( 55,196)( 56,202)( 57,203)( 58,201)
( 59,200)( 60,214)( 61,215)( 62,213)( 63,212)( 64,218)( 65,219)( 66,217)
( 67,216)( 68,206)( 69,207)( 70,205)( 71,204)( 72,210)( 73,211)( 74,209)
( 75,208)( 76,223)( 77,222)( 78,220)( 79,221)( 80,227)( 81,226)( 82,224)
( 83,225)( 84,239)( 85,238)( 86,236)( 87,237)( 88,243)( 89,242)( 90,240)
( 91,241)( 92,231)( 93,230)( 94,228)( 95,229)( 96,235)( 97,234)( 98,232)
( 99,233)(100,247)(101,246)(102,244)(103,245)(104,251)(105,250)(106,248)
(107,249)(108,263)(109,262)(110,260)(111,261)(112,267)(113,266)(114,264)
(115,265)(116,255)(117,254)(118,252)(119,253)(120,259)(121,258)(122,256)
(123,257)(124,271)(125,270)(126,268)(127,269)(128,275)(129,274)(130,272)
(131,273)(132,287)(133,286)(134,284)(135,285)(136,291)(137,290)(138,288)
(139,289)(140,279)(141,278)(142,276)(143,277)(144,283)(145,282)(146,280)
(147,281);
s3 := Sym(291)!( 4,228)( 5,229)( 6,232)( 7,233)( 8,230)( 9,231)( 10,235)
( 11,234)( 12,220)( 13,221)( 14,224)( 15,225)( 16,222)( 17,223)( 18,227)
( 19,226)( 20,236)( 21,237)( 22,240)( 23,241)( 24,238)( 25,239)( 26,243)
( 27,242)( 28,276)( 29,277)( 30,280)( 31,281)( 32,278)( 33,279)( 34,283)
( 35,282)( 36,268)( 37,269)( 38,272)( 39,273)( 40,270)( 41,271)( 42,275)
( 43,274)( 44,284)( 45,285)( 46,288)( 47,289)( 48,286)( 49,287)( 50,291)
( 51,290)( 52,252)( 53,253)( 54,256)( 55,257)( 56,254)( 57,255)( 58,259)
( 59,258)( 60,244)( 61,245)( 62,248)( 63,249)( 64,246)( 65,247)( 66,251)
( 67,250)( 68,260)( 69,261)( 70,264)( 71,265)( 72,262)( 73,263)( 74,267)
( 75,266)( 76,157)( 77,156)( 78,161)( 79,160)( 80,159)( 81,158)( 82,162)
( 83,163)( 84,149)( 85,148)( 86,153)( 87,152)( 88,151)( 89,150)( 90,154)
( 91,155)( 92,165)( 93,164)( 94,169)( 95,168)( 96,167)( 97,166)( 98,170)
( 99,171)(100,205)(101,204)(102,209)(103,208)(104,207)(105,206)(106,210)
(107,211)(108,197)(109,196)(110,201)(111,200)(112,199)(113,198)(114,202)
(115,203)(116,213)(117,212)(118,217)(119,216)(120,215)(121,214)(122,218)
(123,219)(124,181)(125,180)(126,185)(127,184)(128,183)(129,182)(130,186)
(131,187)(132,173)(133,172)(134,177)(135,176)(136,175)(137,174)(138,178)
(139,179)(140,189)(141,188)(142,193)(143,192)(144,191)(145,190)(146,194)
(147,195);
s4 := Sym(291)!( 4,244)( 5,245)( 6,247)( 7,246)( 8,250)( 9,251)( 10,248)
( 11,249)( 12,260)( 13,261)( 14,263)( 15,262)( 16,266)( 17,267)( 18,264)
( 19,265)( 20,252)( 21,253)( 22,255)( 23,254)( 24,258)( 25,259)( 26,256)
( 27,257)( 28,220)( 29,221)( 30,223)( 31,222)( 32,226)( 33,227)( 34,224)
( 35,225)( 36,236)( 37,237)( 38,239)( 39,238)( 40,242)( 41,243)( 42,240)
( 43,241)( 44,228)( 45,229)( 46,231)( 47,230)( 48,234)( 49,235)( 50,232)
( 51,233)( 52,268)( 53,269)( 54,271)( 55,270)( 56,274)( 57,275)( 58,272)
( 59,273)( 60,284)( 61,285)( 62,287)( 63,286)( 64,290)( 65,291)( 66,288)
( 67,289)( 68,276)( 69,277)( 70,279)( 71,278)( 72,282)( 73,283)( 74,280)
( 75,281)( 76,173)( 77,172)( 78,174)( 79,175)( 80,179)( 81,178)( 82,177)
( 83,176)( 84,189)( 85,188)( 86,190)( 87,191)( 88,195)( 89,194)( 90,193)
( 91,192)( 92,181)( 93,180)( 94,182)( 95,183)( 96,187)( 97,186)( 98,185)
( 99,184)(100,149)(101,148)(102,150)(103,151)(104,155)(105,154)(106,153)
(107,152)(108,165)(109,164)(110,166)(111,167)(112,171)(113,170)(114,169)
(115,168)(116,157)(117,156)(118,158)(119,159)(120,163)(121,162)(122,161)
(123,160)(124,197)(125,196)(126,198)(127,199)(128,203)(129,202)(130,201)
(131,200)(132,213)(133,212)(134,214)(135,215)(136,219)(137,218)(138,217)
(139,216)(140,205)(141,204)(142,206)(143,207)(144,211)(145,210)(146,209)
(147,208);
poly := sub<Sym(291)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4, s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope