Polytope of Type {2,2,3,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,3,24}*1152
if this polytope has a name.
Group : SmallGroup(1152,157570)
Rank : 5
Schlafli Type : {2,2,3,24}
Number of vertices, edges, etc : 2, 2, 6, 72, 48
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 : {2,2,3,12}*576
3-fold quotients : {2,2,3,8}*384
6-fold quotients : {2,2,3,4}*192
8-fold quotients : {2,2,3,6}*144
12-fold quotients : {2,2,3,4}*96
24-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5,221)( 6,222)( 7,225)( 8,226)( 9,223)( 10,224)( 11,228)( 12,227)
( 13,237)( 14,238)( 15,241)( 16,242)( 17,239)( 18,240)( 19,244)( 20,243)
( 21,229)( 22,230)( 23,233)( 24,234)( 25,231)( 26,232)( 27,236)( 28,235)
( 29,269)( 30,270)( 31,273)( 32,274)( 33,271)( 34,272)( 35,276)( 36,275)
( 37,285)( 38,286)( 39,289)( 40,290)( 41,287)( 42,288)( 43,292)( 44,291)
( 45,277)( 46,278)( 47,281)( 48,282)( 49,279)( 50,280)( 51,284)( 52,283)
( 53,245)( 54,246)( 55,249)( 56,250)( 57,247)( 58,248)( 59,252)( 60,251)
( 61,261)( 62,262)( 63,265)( 64,266)( 65,263)( 66,264)( 67,268)( 68,267)
( 69,253)( 70,254)( 71,257)( 72,258)( 73,255)( 74,256)( 75,260)( 76,259)
( 77,150)( 78,149)( 79,154)( 80,153)( 81,152)( 82,151)( 83,155)( 84,156)
( 85,166)( 86,165)( 87,170)( 88,169)( 89,168)( 90,167)( 91,171)( 92,172)
( 93,158)( 94,157)( 95,162)( 96,161)( 97,160)( 98,159)( 99,163)(100,164)
(101,198)(102,197)(103,202)(104,201)(105,200)(106,199)(107,203)(108,204)
(109,214)(110,213)(111,218)(112,217)(113,216)(114,215)(115,219)(116,220)
(117,206)(118,205)(119,210)(120,209)(121,208)(122,207)(123,211)(124,212)
(125,174)(126,173)(127,178)(128,177)(129,176)(130,175)(131,179)(132,180)
(133,190)(134,189)(135,194)(136,193)(137,192)(138,191)(139,195)(140,196)
(141,182)(142,181)(143,186)(144,185)(145,184)(146,183)(147,187)(148,188);;
s3 := ( 5,253)( 6,254)( 7,256)( 8,255)( 9,259)( 10,260)( 11,257)( 12,258)
( 13,245)( 14,246)( 15,248)( 16,247)( 17,251)( 18,252)( 19,249)( 20,250)
( 21,261)( 22,262)( 23,264)( 24,263)( 25,267)( 26,268)( 27,265)( 28,266)
( 29,229)( 30,230)( 31,232)( 32,231)( 33,235)( 34,236)( 35,233)( 36,234)
( 37,221)( 38,222)( 39,224)( 40,223)( 41,227)( 42,228)( 43,225)( 44,226)
( 45,237)( 46,238)( 47,240)( 48,239)( 49,243)( 50,244)( 51,241)( 52,242)
( 53,277)( 54,278)( 55,280)( 56,279)( 57,283)( 58,284)( 59,281)( 60,282)
( 61,269)( 62,270)( 63,272)( 64,271)( 65,275)( 66,276)( 67,273)( 68,274)
( 69,285)( 70,286)( 71,288)( 72,287)( 73,291)( 74,292)( 75,289)( 76,290)
( 77,182)( 78,181)( 79,183)( 80,184)( 81,188)( 82,187)( 83,186)( 84,185)
( 85,174)( 86,173)( 87,175)( 88,176)( 89,180)( 90,179)( 91,178)( 92,177)
( 93,190)( 94,189)( 95,191)( 96,192)( 97,196)( 98,195)( 99,194)(100,193)
(101,158)(102,157)(103,159)(104,160)(105,164)(106,163)(107,162)(108,161)
(109,150)(110,149)(111,151)(112,152)(113,156)(114,155)(115,154)(116,153)
(117,166)(118,165)(119,167)(120,168)(121,172)(122,171)(123,170)(124,169)
(125,206)(126,205)(127,207)(128,208)(129,212)(130,211)(131,210)(132,209)
(133,198)(134,197)(135,199)(136,200)(137,204)(138,203)(139,202)(140,201)
(141,214)(142,213)(143,215)(144,216)(145,220)(146,219)(147,218)(148,217);;
s4 := ( 5,155)( 6,156)( 7,153)( 8,154)( 9,152)( 10,151)( 11,150)( 12,149)
( 13,171)( 14,172)( 15,169)( 16,170)( 17,168)( 18,167)( 19,166)( 20,165)
( 21,163)( 22,164)( 23,161)( 24,162)( 25,160)( 26,159)( 27,158)( 28,157)
( 29,179)( 30,180)( 31,177)( 32,178)( 33,176)( 34,175)( 35,174)( 36,173)
( 37,195)( 38,196)( 39,193)( 40,194)( 41,192)( 42,191)( 43,190)( 44,189)
( 45,187)( 46,188)( 47,185)( 48,186)( 49,184)( 50,183)( 51,182)( 52,181)
( 53,203)( 54,204)( 55,201)( 56,202)( 57,200)( 58,199)( 59,198)( 60,197)
( 61,219)( 62,220)( 63,217)( 64,218)( 65,216)( 66,215)( 67,214)( 68,213)
( 69,211)( 70,212)( 71,209)( 72,210)( 73,208)( 74,207)( 75,206)( 76,205)
( 77,228)( 78,227)( 79,226)( 80,225)( 81,223)( 82,224)( 83,221)( 84,222)
( 85,244)( 86,243)( 87,242)( 88,241)( 89,239)( 90,240)( 91,237)( 92,238)
( 93,236)( 94,235)( 95,234)( 96,233)( 97,231)( 98,232)( 99,229)(100,230)
(101,252)(102,251)(103,250)(104,249)(105,247)(106,248)(107,245)(108,246)
(109,268)(110,267)(111,266)(112,265)(113,263)(114,264)(115,261)(116,262)
(117,260)(118,259)(119,258)(120,257)(121,255)(122,256)(123,253)(124,254)
(125,276)(126,275)(127,274)(128,273)(129,271)(130,272)(131,269)(132,270)
(133,292)(134,291)(135,290)(136,289)(137,287)(138,288)(139,285)(140,286)
(141,284)(142,283)(143,282)(144,281)(145,279)(146,280)(147,277)(148,278);;
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*s1*s0*s1,
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, s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(292)!(1,2);
s1 := Sym(292)!(3,4);
s2 := Sym(292)!( 5,221)( 6,222)( 7,225)( 8,226)( 9,223)( 10,224)( 11,228)
( 12,227)( 13,237)( 14,238)( 15,241)( 16,242)( 17,239)( 18,240)( 19,244)
( 20,243)( 21,229)( 22,230)( 23,233)( 24,234)( 25,231)( 26,232)( 27,236)
( 28,235)( 29,269)( 30,270)( 31,273)( 32,274)( 33,271)( 34,272)( 35,276)
( 36,275)( 37,285)( 38,286)( 39,289)( 40,290)( 41,287)( 42,288)( 43,292)
( 44,291)( 45,277)( 46,278)( 47,281)( 48,282)( 49,279)( 50,280)( 51,284)
( 52,283)( 53,245)( 54,246)( 55,249)( 56,250)( 57,247)( 58,248)( 59,252)
( 60,251)( 61,261)( 62,262)( 63,265)( 64,266)( 65,263)( 66,264)( 67,268)
( 68,267)( 69,253)( 70,254)( 71,257)( 72,258)( 73,255)( 74,256)( 75,260)
( 76,259)( 77,150)( 78,149)( 79,154)( 80,153)( 81,152)( 82,151)( 83,155)
( 84,156)( 85,166)( 86,165)( 87,170)( 88,169)( 89,168)( 90,167)( 91,171)
( 92,172)( 93,158)( 94,157)( 95,162)( 96,161)( 97,160)( 98,159)( 99,163)
(100,164)(101,198)(102,197)(103,202)(104,201)(105,200)(106,199)(107,203)
(108,204)(109,214)(110,213)(111,218)(112,217)(113,216)(114,215)(115,219)
(116,220)(117,206)(118,205)(119,210)(120,209)(121,208)(122,207)(123,211)
(124,212)(125,174)(126,173)(127,178)(128,177)(129,176)(130,175)(131,179)
(132,180)(133,190)(134,189)(135,194)(136,193)(137,192)(138,191)(139,195)
(140,196)(141,182)(142,181)(143,186)(144,185)(145,184)(146,183)(147,187)
(148,188);
s3 := Sym(292)!( 5,253)( 6,254)( 7,256)( 8,255)( 9,259)( 10,260)( 11,257)
( 12,258)( 13,245)( 14,246)( 15,248)( 16,247)( 17,251)( 18,252)( 19,249)
( 20,250)( 21,261)( 22,262)( 23,264)( 24,263)( 25,267)( 26,268)( 27,265)
( 28,266)( 29,229)( 30,230)( 31,232)( 32,231)( 33,235)( 34,236)( 35,233)
( 36,234)( 37,221)( 38,222)( 39,224)( 40,223)( 41,227)( 42,228)( 43,225)
( 44,226)( 45,237)( 46,238)( 47,240)( 48,239)( 49,243)( 50,244)( 51,241)
( 52,242)( 53,277)( 54,278)( 55,280)( 56,279)( 57,283)( 58,284)( 59,281)
( 60,282)( 61,269)( 62,270)( 63,272)( 64,271)( 65,275)( 66,276)( 67,273)
( 68,274)( 69,285)( 70,286)( 71,288)( 72,287)( 73,291)( 74,292)( 75,289)
( 76,290)( 77,182)( 78,181)( 79,183)( 80,184)( 81,188)( 82,187)( 83,186)
( 84,185)( 85,174)( 86,173)( 87,175)( 88,176)( 89,180)( 90,179)( 91,178)
( 92,177)( 93,190)( 94,189)( 95,191)( 96,192)( 97,196)( 98,195)( 99,194)
(100,193)(101,158)(102,157)(103,159)(104,160)(105,164)(106,163)(107,162)
(108,161)(109,150)(110,149)(111,151)(112,152)(113,156)(114,155)(115,154)
(116,153)(117,166)(118,165)(119,167)(120,168)(121,172)(122,171)(123,170)
(124,169)(125,206)(126,205)(127,207)(128,208)(129,212)(130,211)(131,210)
(132,209)(133,198)(134,197)(135,199)(136,200)(137,204)(138,203)(139,202)
(140,201)(141,214)(142,213)(143,215)(144,216)(145,220)(146,219)(147,218)
(148,217);
s4 := Sym(292)!( 5,155)( 6,156)( 7,153)( 8,154)( 9,152)( 10,151)( 11,150)
( 12,149)( 13,171)( 14,172)( 15,169)( 16,170)( 17,168)( 18,167)( 19,166)
( 20,165)( 21,163)( 22,164)( 23,161)( 24,162)( 25,160)( 26,159)( 27,158)
( 28,157)( 29,179)( 30,180)( 31,177)( 32,178)( 33,176)( 34,175)( 35,174)
( 36,173)( 37,195)( 38,196)( 39,193)( 40,194)( 41,192)( 42,191)( 43,190)
( 44,189)( 45,187)( 46,188)( 47,185)( 48,186)( 49,184)( 50,183)( 51,182)
( 52,181)( 53,203)( 54,204)( 55,201)( 56,202)( 57,200)( 58,199)( 59,198)
( 60,197)( 61,219)( 62,220)( 63,217)( 64,218)( 65,216)( 66,215)( 67,214)
( 68,213)( 69,211)( 70,212)( 71,209)( 72,210)( 73,208)( 74,207)( 75,206)
( 76,205)( 77,228)( 78,227)( 79,226)( 80,225)( 81,223)( 82,224)( 83,221)
( 84,222)( 85,244)( 86,243)( 87,242)( 88,241)( 89,239)( 90,240)( 91,237)
( 92,238)( 93,236)( 94,235)( 95,234)( 96,233)( 97,231)( 98,232)( 99,229)
(100,230)(101,252)(102,251)(103,250)(104,249)(105,247)(106,248)(107,245)
(108,246)(109,268)(110,267)(111,266)(112,265)(113,263)(114,264)(115,261)
(116,262)(117,260)(118,259)(119,258)(120,257)(121,255)(122,256)(123,253)
(124,254)(125,276)(126,275)(127,274)(128,273)(129,271)(130,272)(131,269)
(132,270)(133,292)(134,291)(135,290)(136,289)(137,287)(138,288)(139,285)
(140,286)(141,284)(142,283)(143,282)(144,281)(145,279)(146,280)(147,277)
(148,278);
poly := sub<Sym(292)|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*s1*s0*s1, 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,
s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3*s4*s3 >;
to this polytope