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