Polytope of Type {2,2,24,3}

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