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Polytope of Type {250}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {250}*500
Also Known As : 250-gon, {250}. if this polytope has another name.
Group : SmallGroup(500,4)
Rank : 2
Schlafli Type : {250}
Number of vertices, edges, etc : 250, 250
Order of s0s1 : 250
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {250,2} of size 1000
   {250,4} of size 2000
Vertex Figure Of :
   {2,250} of size 1000
   {4,250} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {125}*250
   5-fold quotients : {50}*100
   10-fold quotients : {25}*50
   25-fold quotients : {10}*20
   50-fold quotients : {5}*10
   125-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {500}*1000
   3-fold covers : {750}*1500
   4-fold covers : {1000}*2000
Permutation Representation (GAP) :
s0 := (  2,  5)(  3,  4)(  6, 22)(  7, 21)(  8, 25)(  9, 24)( 10, 23)( 11, 17)
( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26,106)( 27,110)( 28,109)( 29,108)
( 30,107)( 31,101)( 32,105)( 33,104)( 34,103)( 35,102)( 36,122)( 37,121)
( 38,125)( 39,124)( 40,123)( 41,117)( 42,116)( 43,120)( 44,119)( 45,118)
( 46,112)( 47,111)( 48,115)( 49,114)( 50,113)( 51, 81)( 52, 85)( 53, 84)
( 54, 83)( 55, 82)( 56, 76)( 57, 80)( 58, 79)( 59, 78)( 60, 77)( 61, 97)
( 62, 96)( 63,100)( 64, 99)( 65, 98)( 66, 92)( 67, 91)( 68, 95)( 69, 94)
( 70, 93)( 71, 87)( 72, 86)( 73, 90)( 74, 89)( 75, 88)(127,130)(128,129)
(131,147)(132,146)(133,150)(134,149)(135,148)(136,142)(137,141)(138,145)
(139,144)(140,143)(151,231)(152,235)(153,234)(154,233)(155,232)(156,226)
(157,230)(158,229)(159,228)(160,227)(161,247)(162,246)(163,250)(164,249)
(165,248)(166,242)(167,241)(168,245)(169,244)(170,243)(171,237)(172,236)
(173,240)(174,239)(175,238)(176,206)(177,210)(178,209)(179,208)(180,207)
(181,201)(182,205)(183,204)(184,203)(185,202)(186,222)(187,221)(188,225)
(189,224)(190,223)(191,217)(192,216)(193,220)(194,219)(195,218)(196,212)
(197,211)(198,215)(199,214)(200,213);;
s1 := (  1,151)(  2,155)(  3,154)(  4,153)(  5,152)(  6,172)(  7,171)(  8,175)
(  9,174)( 10,173)( 11,167)( 12,166)( 13,170)( 14,169)( 15,168)( 16,162)
( 17,161)( 18,165)( 19,164)( 20,163)( 21,157)( 22,156)( 23,160)( 24,159)
( 25,158)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,147)( 32,146)
( 33,150)( 34,149)( 35,148)( 36,142)( 37,141)( 38,145)( 39,144)( 40,143)
( 41,137)( 42,136)( 43,140)( 44,139)( 45,138)( 46,132)( 47,131)( 48,135)
( 49,134)( 50,133)( 51,231)( 52,235)( 53,234)( 54,233)( 55,232)( 56,226)
( 57,230)( 58,229)( 59,228)( 60,227)( 61,247)( 62,246)( 63,250)( 64,249)
( 65,248)( 66,242)( 67,241)( 68,245)( 69,244)( 70,243)( 71,237)( 72,236)
( 73,240)( 74,239)( 75,238)( 76,206)( 77,210)( 78,209)( 79,208)( 80,207)
( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,222)( 87,221)( 88,225)
( 89,224)( 90,223)( 91,217)( 92,216)( 93,220)( 94,219)( 95,218)( 96,212)
( 97,211)( 98,215)( 99,214)(100,213)(101,181)(102,185)(103,184)(104,183)
(105,182)(106,176)(107,180)(108,179)(109,178)(110,177)(111,197)(112,196)
(113,200)(114,199)(115,198)(116,192)(117,191)(118,195)(119,194)(120,193)
(121,187)(122,186)(123,190)(124,189)(125,188);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(250)!(  2,  5)(  3,  4)(  6, 22)(  7, 21)(  8, 25)(  9, 24)( 10, 23)
( 11, 17)( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26,106)( 27,110)( 28,109)
( 29,108)( 30,107)( 31,101)( 32,105)( 33,104)( 34,103)( 35,102)( 36,122)
( 37,121)( 38,125)( 39,124)( 40,123)( 41,117)( 42,116)( 43,120)( 44,119)
( 45,118)( 46,112)( 47,111)( 48,115)( 49,114)( 50,113)( 51, 81)( 52, 85)
( 53, 84)( 54, 83)( 55, 82)( 56, 76)( 57, 80)( 58, 79)( 59, 78)( 60, 77)
( 61, 97)( 62, 96)( 63,100)( 64, 99)( 65, 98)( 66, 92)( 67, 91)( 68, 95)
( 69, 94)( 70, 93)( 71, 87)( 72, 86)( 73, 90)( 74, 89)( 75, 88)(127,130)
(128,129)(131,147)(132,146)(133,150)(134,149)(135,148)(136,142)(137,141)
(138,145)(139,144)(140,143)(151,231)(152,235)(153,234)(154,233)(155,232)
(156,226)(157,230)(158,229)(159,228)(160,227)(161,247)(162,246)(163,250)
(164,249)(165,248)(166,242)(167,241)(168,245)(169,244)(170,243)(171,237)
(172,236)(173,240)(174,239)(175,238)(176,206)(177,210)(178,209)(179,208)
(180,207)(181,201)(182,205)(183,204)(184,203)(185,202)(186,222)(187,221)
(188,225)(189,224)(190,223)(191,217)(192,216)(193,220)(194,219)(195,218)
(196,212)(197,211)(198,215)(199,214)(200,213);
s1 := Sym(250)!(  1,151)(  2,155)(  3,154)(  4,153)(  5,152)(  6,172)(  7,171)
(  8,175)(  9,174)( 10,173)( 11,167)( 12,166)( 13,170)( 14,169)( 15,168)
( 16,162)( 17,161)( 18,165)( 19,164)( 20,163)( 21,157)( 22,156)( 23,160)
( 24,159)( 25,158)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,147)
( 32,146)( 33,150)( 34,149)( 35,148)( 36,142)( 37,141)( 38,145)( 39,144)
( 40,143)( 41,137)( 42,136)( 43,140)( 44,139)( 45,138)( 46,132)( 47,131)
( 48,135)( 49,134)( 50,133)( 51,231)( 52,235)( 53,234)( 54,233)( 55,232)
( 56,226)( 57,230)( 58,229)( 59,228)( 60,227)( 61,247)( 62,246)( 63,250)
( 64,249)( 65,248)( 66,242)( 67,241)( 68,245)( 69,244)( 70,243)( 71,237)
( 72,236)( 73,240)( 74,239)( 75,238)( 76,206)( 77,210)( 78,209)( 79,208)
( 80,207)( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,222)( 87,221)
( 88,225)( 89,224)( 90,223)( 91,217)( 92,216)( 93,220)( 94,219)( 95,218)
( 96,212)( 97,211)( 98,215)( 99,214)(100,213)(101,181)(102,185)(103,184)
(104,183)(105,182)(106,176)(107,180)(108,179)(109,178)(110,177)(111,197)
(112,196)(113,200)(114,199)(115,198)(116,192)(117,191)(118,195)(119,194)
(120,193)(121,187)(122,186)(123,190)(124,189)(125,188);
poly := sub<Sym(250)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope