Polytope of Type {10,5,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,5,2}*640b
if this polytope has a name.
Group : SmallGroup(640,21537)
Rank : 4
Schlafli Type : {10,5,2}
Number of vertices, edges, etc : 32, 80, 16, 2
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,5,2,2} of size 1280
   {10,5,2,3} of size 1920
Vertex Figure Of :
   {2,10,5,2} of size 1280
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,5,2}*320
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,5,2}*1280, {10,10,2}*1280c, {20,5,2}*1280a, {20,5,2}*1280b, {10,10,2}*1280d
   3-fold covers : {10,15,2}*1920
Permutation Representation (GAP) : 
s0 := (  1,161)(  2,171)(  3,174)(  4,168)(  5,165)(  6,175)(  7,170)(  8,164)
(  9,173)( 10,167)( 11,162)( 12,172)( 13,169)( 14,163)( 15,166)( 16,176)
( 17,225)( 18,235)( 19,238)( 20,232)( 21,229)( 22,239)( 23,234)( 24,228)
( 25,237)( 26,231)( 27,226)( 28,236)( 29,233)( 30,227)( 31,230)( 32,240)
( 33,209)( 34,219)( 35,222)( 36,216)( 37,213)( 38,223)( 39,218)( 40,212)
( 41,221)( 42,215)( 43,210)( 44,220)( 45,217)( 46,211)( 47,214)( 48,224)
( 49,193)( 50,203)( 51,206)( 52,200)( 53,197)( 54,207)( 55,202)( 56,196)
( 57,205)( 58,199)( 59,194)( 60,204)( 61,201)( 62,195)( 63,198)( 64,208)
( 65,177)( 66,187)( 67,190)( 68,184)( 69,181)( 70,191)( 71,186)( 72,180)
( 73,189)( 74,183)( 75,178)( 76,188)( 77,185)( 78,179)( 79,182)( 80,192)
( 81,241)( 82,251)( 83,254)( 84,248)( 85,245)( 86,255)( 87,250)( 88,244)
( 89,253)( 90,247)( 91,242)( 92,252)( 93,249)( 94,243)( 95,246)( 96,256)
( 97,305)( 98,315)( 99,318)(100,312)(101,309)(102,319)(103,314)(104,308)
(105,317)(106,311)(107,306)(108,316)(109,313)(110,307)(111,310)(112,320)
(113,289)(114,299)(115,302)(116,296)(117,293)(118,303)(119,298)(120,292)
(121,301)(122,295)(123,290)(124,300)(125,297)(126,291)(127,294)(128,304)
(129,273)(130,283)(131,286)(132,280)(133,277)(134,287)(135,282)(136,276)
(137,285)(138,279)(139,274)(140,284)(141,281)(142,275)(143,278)(144,288)
(145,257)(146,267)(147,270)(148,264)(149,261)(150,271)(151,266)(152,260)
(153,269)(154,263)(155,258)(156,268)(157,265)(158,259)(159,262)(160,272);;
s1 := (  1,257)(  2,272)(  3,259)(  4,270)(  5,263)(  6,266)(  7,261)(  8,268)
(  9,267)( 10,262)( 11,265)( 12,264)( 13,269)( 14,260)( 15,271)( 16,258)
( 17,241)( 18,256)( 19,243)( 20,254)( 21,247)( 22,250)( 23,245)( 24,252)
( 25,251)( 26,246)( 27,249)( 28,248)( 29,253)( 30,244)( 31,255)( 32,242)
( 33,305)( 34,320)( 35,307)( 36,318)( 37,311)( 38,314)( 39,309)( 40,316)
( 41,315)( 42,310)( 43,313)( 44,312)( 45,317)( 46,308)( 47,319)( 48,306)
( 49,289)( 50,304)( 51,291)( 52,302)( 53,295)( 54,298)( 55,293)( 56,300)
( 57,299)( 58,294)( 59,297)( 60,296)( 61,301)( 62,292)( 63,303)( 64,290)
( 65,273)( 66,288)( 67,275)( 68,286)( 69,279)( 70,282)( 71,277)( 72,284)
( 73,283)( 74,278)( 75,281)( 76,280)( 77,285)( 78,276)( 79,287)( 80,274)
( 81,177)( 82,192)( 83,179)( 84,190)( 85,183)( 86,186)( 87,181)( 88,188)
( 89,187)( 90,182)( 91,185)( 92,184)( 93,189)( 94,180)( 95,191)( 96,178)
( 97,161)( 98,176)( 99,163)(100,174)(101,167)(102,170)(103,165)(104,172)
(105,171)(106,166)(107,169)(108,168)(109,173)(110,164)(111,175)(112,162)
(113,225)(114,240)(115,227)(116,238)(117,231)(118,234)(119,229)(120,236)
(121,235)(122,230)(123,233)(124,232)(125,237)(126,228)(127,239)(128,226)
(129,209)(130,224)(131,211)(132,222)(133,215)(134,218)(135,213)(136,220)
(137,219)(138,214)(139,217)(140,216)(141,221)(142,212)(143,223)(144,210)
(145,193)(146,208)(147,195)(148,206)(149,199)(150,202)(151,197)(152,204)
(153,203)(154,198)(155,201)(156,200)(157,205)(158,196)(159,207)(160,194);;
s2 := (  1,245)(  2,255)(  3,250)(  4,244)(  5,241)(  6,251)(  7,254)(  8,248)
(  9,249)( 10,243)( 11,246)( 12,256)( 13,253)( 14,247)( 15,242)( 16,252)
( 17,309)( 18,319)( 19,314)( 20,308)( 21,305)( 22,315)( 23,318)( 24,312)
( 25,313)( 26,307)( 27,310)( 28,320)( 29,317)( 30,311)( 31,306)( 32,316)
( 33,293)( 34,303)( 35,298)( 36,292)( 37,289)( 38,299)( 39,302)( 40,296)
( 41,297)( 42,291)( 43,294)( 44,304)( 45,301)( 46,295)( 47,290)( 48,300)
( 49,277)( 50,287)( 51,282)( 52,276)( 53,273)( 54,283)( 55,286)( 56,280)
( 57,281)( 58,275)( 59,278)( 60,288)( 61,285)( 62,279)( 63,274)( 64,284)
( 65,261)( 66,271)( 67,266)( 68,260)( 69,257)( 70,267)( 71,270)( 72,264)
( 73,265)( 74,259)( 75,262)( 76,272)( 77,269)( 78,263)( 79,258)( 80,268)
( 81,165)( 82,175)( 83,170)( 84,164)( 85,161)( 86,171)( 87,174)( 88,168)
( 89,169)( 90,163)( 91,166)( 92,176)( 93,173)( 94,167)( 95,162)( 96,172)
( 97,229)( 98,239)( 99,234)(100,228)(101,225)(102,235)(103,238)(104,232)
(105,233)(106,227)(107,230)(108,240)(109,237)(110,231)(111,226)(112,236)
(113,213)(114,223)(115,218)(116,212)(117,209)(118,219)(119,222)(120,216)
(121,217)(122,211)(123,214)(124,224)(125,221)(126,215)(127,210)(128,220)
(129,197)(130,207)(131,202)(132,196)(133,193)(134,203)(135,206)(136,200)
(137,201)(138,195)(139,198)(140,208)(141,205)(142,199)(143,194)(144,204)
(145,181)(146,191)(147,186)(148,180)(149,177)(150,187)(151,190)(152,184)
(153,185)(154,179)(155,182)(156,192)(157,189)(158,183)(159,178)(160,188);;
s3 := (321,322);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(322)!(  1,161)(  2,171)(  3,174)(  4,168)(  5,165)(  6,175)(  7,170)
(  8,164)(  9,173)( 10,167)( 11,162)( 12,172)( 13,169)( 14,163)( 15,166)
( 16,176)( 17,225)( 18,235)( 19,238)( 20,232)( 21,229)( 22,239)( 23,234)
( 24,228)( 25,237)( 26,231)( 27,226)( 28,236)( 29,233)( 30,227)( 31,230)
( 32,240)( 33,209)( 34,219)( 35,222)( 36,216)( 37,213)( 38,223)( 39,218)
( 40,212)( 41,221)( 42,215)( 43,210)( 44,220)( 45,217)( 46,211)( 47,214)
( 48,224)( 49,193)( 50,203)( 51,206)( 52,200)( 53,197)( 54,207)( 55,202)
( 56,196)( 57,205)( 58,199)( 59,194)( 60,204)( 61,201)( 62,195)( 63,198)
( 64,208)( 65,177)( 66,187)( 67,190)( 68,184)( 69,181)( 70,191)( 71,186)
( 72,180)( 73,189)( 74,183)( 75,178)( 76,188)( 77,185)( 78,179)( 79,182)
( 80,192)( 81,241)( 82,251)( 83,254)( 84,248)( 85,245)( 86,255)( 87,250)
( 88,244)( 89,253)( 90,247)( 91,242)( 92,252)( 93,249)( 94,243)( 95,246)
( 96,256)( 97,305)( 98,315)( 99,318)(100,312)(101,309)(102,319)(103,314)
(104,308)(105,317)(106,311)(107,306)(108,316)(109,313)(110,307)(111,310)
(112,320)(113,289)(114,299)(115,302)(116,296)(117,293)(118,303)(119,298)
(120,292)(121,301)(122,295)(123,290)(124,300)(125,297)(126,291)(127,294)
(128,304)(129,273)(130,283)(131,286)(132,280)(133,277)(134,287)(135,282)
(136,276)(137,285)(138,279)(139,274)(140,284)(141,281)(142,275)(143,278)
(144,288)(145,257)(146,267)(147,270)(148,264)(149,261)(150,271)(151,266)
(152,260)(153,269)(154,263)(155,258)(156,268)(157,265)(158,259)(159,262)
(160,272);
s1 := Sym(322)!(  1,257)(  2,272)(  3,259)(  4,270)(  5,263)(  6,266)(  7,261)
(  8,268)(  9,267)( 10,262)( 11,265)( 12,264)( 13,269)( 14,260)( 15,271)
( 16,258)( 17,241)( 18,256)( 19,243)( 20,254)( 21,247)( 22,250)( 23,245)
( 24,252)( 25,251)( 26,246)( 27,249)( 28,248)( 29,253)( 30,244)( 31,255)
( 32,242)( 33,305)( 34,320)( 35,307)( 36,318)( 37,311)( 38,314)( 39,309)
( 40,316)( 41,315)( 42,310)( 43,313)( 44,312)( 45,317)( 46,308)( 47,319)
( 48,306)( 49,289)( 50,304)( 51,291)( 52,302)( 53,295)( 54,298)( 55,293)
( 56,300)( 57,299)( 58,294)( 59,297)( 60,296)( 61,301)( 62,292)( 63,303)
( 64,290)( 65,273)( 66,288)( 67,275)( 68,286)( 69,279)( 70,282)( 71,277)
( 72,284)( 73,283)( 74,278)( 75,281)( 76,280)( 77,285)( 78,276)( 79,287)
( 80,274)( 81,177)( 82,192)( 83,179)( 84,190)( 85,183)( 86,186)( 87,181)
( 88,188)( 89,187)( 90,182)( 91,185)( 92,184)( 93,189)( 94,180)( 95,191)
( 96,178)( 97,161)( 98,176)( 99,163)(100,174)(101,167)(102,170)(103,165)
(104,172)(105,171)(106,166)(107,169)(108,168)(109,173)(110,164)(111,175)
(112,162)(113,225)(114,240)(115,227)(116,238)(117,231)(118,234)(119,229)
(120,236)(121,235)(122,230)(123,233)(124,232)(125,237)(126,228)(127,239)
(128,226)(129,209)(130,224)(131,211)(132,222)(133,215)(134,218)(135,213)
(136,220)(137,219)(138,214)(139,217)(140,216)(141,221)(142,212)(143,223)
(144,210)(145,193)(146,208)(147,195)(148,206)(149,199)(150,202)(151,197)
(152,204)(153,203)(154,198)(155,201)(156,200)(157,205)(158,196)(159,207)
(160,194);
s2 := Sym(322)!(  1,245)(  2,255)(  3,250)(  4,244)(  5,241)(  6,251)(  7,254)
(  8,248)(  9,249)( 10,243)( 11,246)( 12,256)( 13,253)( 14,247)( 15,242)
( 16,252)( 17,309)( 18,319)( 19,314)( 20,308)( 21,305)( 22,315)( 23,318)
( 24,312)( 25,313)( 26,307)( 27,310)( 28,320)( 29,317)( 30,311)( 31,306)
( 32,316)( 33,293)( 34,303)( 35,298)( 36,292)( 37,289)( 38,299)( 39,302)
( 40,296)( 41,297)( 42,291)( 43,294)( 44,304)( 45,301)( 46,295)( 47,290)
( 48,300)( 49,277)( 50,287)( 51,282)( 52,276)( 53,273)( 54,283)( 55,286)
( 56,280)( 57,281)( 58,275)( 59,278)( 60,288)( 61,285)( 62,279)( 63,274)
( 64,284)( 65,261)( 66,271)( 67,266)( 68,260)( 69,257)( 70,267)( 71,270)
( 72,264)( 73,265)( 74,259)( 75,262)( 76,272)( 77,269)( 78,263)( 79,258)
( 80,268)( 81,165)( 82,175)( 83,170)( 84,164)( 85,161)( 86,171)( 87,174)
( 88,168)( 89,169)( 90,163)( 91,166)( 92,176)( 93,173)( 94,167)( 95,162)
( 96,172)( 97,229)( 98,239)( 99,234)(100,228)(101,225)(102,235)(103,238)
(104,232)(105,233)(106,227)(107,230)(108,240)(109,237)(110,231)(111,226)
(112,236)(113,213)(114,223)(115,218)(116,212)(117,209)(118,219)(119,222)
(120,216)(121,217)(122,211)(123,214)(124,224)(125,221)(126,215)(127,210)
(128,220)(129,197)(130,207)(131,202)(132,196)(133,193)(134,203)(135,206)
(136,200)(137,201)(138,195)(139,198)(140,208)(141,205)(142,199)(143,194)
(144,204)(145,181)(146,191)(147,186)(148,180)(149,177)(150,187)(151,190)
(152,184)(153,185)(154,179)(155,182)(156,192)(157,189)(158,183)(159,178)
(160,188);
s3 := Sym(322)!(321,322);
poly := sub<Sym(322)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope