Polytope of Type {4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10}*2000a
if this polytope has a name.
Group : SmallGroup(2000,482)
Rank : 3
Schlafli Type : {4,10}
Number of vertices, edges, etc : 100, 500, 250
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,10}*1000
   5-fold quotients : {4,10}*400
   10-fold quotients : {4,10}*200
   125-fold quotients : {4,2}*16
   250-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  5)(  3,  4)(  6, 59)(  7, 58)(  8, 57)(  9, 56)( 10, 60)( 11,114)
( 12,113)( 13,112)( 14,111)( 15,115)( 16, 41)( 17, 45)( 18, 44)( 19, 43)
( 20, 42)( 21,100)( 22, 99)( 23, 98)( 24, 97)( 25, 96)( 26,101)( 27,105)
( 28,104)( 29,103)( 30,102)( 31, 34)( 32, 33)( 36, 89)( 37, 88)( 38, 87)
( 39, 86)( 40, 90)( 46, 75)( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 51, 76)
( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 61, 64)( 62, 63)( 66,116)( 67,120)
( 68,119)( 69,118)( 70,117)( 81,109)( 82,108)( 83,107)( 84,106)( 85,110)
( 92, 95)( 93, 94)(121,125)(122,124)(127,130)(128,129)(131,184)(132,183)
(133,182)(134,181)(135,185)(136,239)(137,238)(138,237)(139,236)(140,240)
(141,166)(142,170)(143,169)(144,168)(145,167)(146,225)(147,224)(148,223)
(149,222)(150,221)(151,226)(152,230)(153,229)(154,228)(155,227)(156,159)
(157,158)(161,214)(162,213)(163,212)(164,211)(165,215)(171,200)(172,199)
(173,198)(174,197)(175,196)(176,201)(177,205)(178,204)(179,203)(180,202)
(186,189)(187,188)(191,241)(192,245)(193,244)(194,243)(195,242)(206,234)
(207,233)(208,232)(209,231)(210,235)(217,220)(218,219)(246,250)(247,249);;
s1 := (  2,  5)(  3,  4)(  6, 41)(  7, 45)(  8, 44)(  9, 43)( 10, 42)( 11, 59)
( 12, 58)( 13, 57)( 14, 56)( 15, 60)( 16,100)( 17, 99)( 18, 98)( 19, 97)
( 20, 96)( 21,114)( 22,113)( 23,112)( 24,111)( 25,115)( 26, 61)( 27, 65)
( 28, 64)( 29, 63)( 30, 62)( 31, 78)( 32, 77)( 33, 76)( 34, 80)( 35, 79)
( 36,118)( 37,117)( 38,116)( 39,120)( 40,119)( 46, 47)( 48, 50)( 51,125)
( 52,124)( 53,123)( 54,122)( 55,121)( 67, 70)( 68, 69)( 71, 84)( 72, 83)
( 73, 82)( 74, 81)( 75, 85)( 86, 88)( 89, 90)( 91,105)( 92,104)( 93,103)
( 94,102)( 95,101)(106,108)(109,110)(127,130)(128,129)(131,166)(132,170)
(133,169)(134,168)(135,167)(136,184)(137,183)(138,182)(139,181)(140,185)
(141,225)(142,224)(143,223)(144,222)(145,221)(146,239)(147,238)(148,237)
(149,236)(150,240)(151,186)(152,190)(153,189)(154,188)(155,187)(156,203)
(157,202)(158,201)(159,205)(160,204)(161,243)(162,242)(163,241)(164,245)
(165,244)(171,172)(173,175)(176,250)(177,249)(178,248)(179,247)(180,246)
(192,195)(193,194)(196,209)(197,208)(198,207)(199,206)(200,210)(211,213)
(214,215)(216,230)(217,229)(218,228)(219,227)(220,226)(231,233)(234,235);;
s2 := (  1,216)(  2,217)(  3,218)(  4,219)(  5,220)(  6,213)(  7,214)(  8,215)
(  9,211)( 10,212)( 11,210)( 12,206)( 13,207)( 14,208)( 15,209)( 16,202)
( 17,203)( 18,204)( 19,205)( 20,201)( 21,224)( 22,225)( 23,221)( 24,222)
( 25,223)( 26,194)( 27,195)( 28,191)( 29,192)( 30,193)( 31,186)( 32,187)
( 33,188)( 34,189)( 35,190)( 36,183)( 37,184)( 38,185)( 39,181)( 40,182)
( 41,180)( 42,176)( 43,177)( 44,178)( 45,179)( 46,197)( 47,198)( 48,199)
( 49,200)( 50,196)( 51,167)( 52,168)( 53,169)( 54,170)( 55,166)( 56,164)
( 57,165)( 58,161)( 59,162)( 60,163)( 61,156)( 62,157)( 63,158)( 64,159)
( 65,160)( 66,153)( 67,154)( 68,155)( 69,151)( 70,152)( 71,175)( 72,171)
( 73,172)( 74,173)( 75,174)( 76,145)( 77,141)( 78,142)( 79,143)( 80,144)
( 81,137)( 82,138)( 83,139)( 84,140)( 85,136)( 86,134)( 87,135)( 88,131)
( 89,132)( 90,133)( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)( 96,148)
( 97,149)( 98,150)( 99,146)(100,147)(101,243)(102,244)(103,245)(104,241)
(105,242)(106,240)(107,236)(108,237)(109,238)(110,239)(111,232)(112,233)
(113,234)(114,235)(115,231)(116,229)(117,230)(118,226)(119,227)(120,228)
(121,246)(122,247)(123,248)(124,249)(125,250);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(250)!(  2,  5)(  3,  4)(  6, 59)(  7, 58)(  8, 57)(  9, 56)( 10, 60)
( 11,114)( 12,113)( 13,112)( 14,111)( 15,115)( 16, 41)( 17, 45)( 18, 44)
( 19, 43)( 20, 42)( 21,100)( 22, 99)( 23, 98)( 24, 97)( 25, 96)( 26,101)
( 27,105)( 28,104)( 29,103)( 30,102)( 31, 34)( 32, 33)( 36, 89)( 37, 88)
( 38, 87)( 39, 86)( 40, 90)( 46, 75)( 47, 74)( 48, 73)( 49, 72)( 50, 71)
( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 61, 64)( 62, 63)( 66,116)
( 67,120)( 68,119)( 69,118)( 70,117)( 81,109)( 82,108)( 83,107)( 84,106)
( 85,110)( 92, 95)( 93, 94)(121,125)(122,124)(127,130)(128,129)(131,184)
(132,183)(133,182)(134,181)(135,185)(136,239)(137,238)(138,237)(139,236)
(140,240)(141,166)(142,170)(143,169)(144,168)(145,167)(146,225)(147,224)
(148,223)(149,222)(150,221)(151,226)(152,230)(153,229)(154,228)(155,227)
(156,159)(157,158)(161,214)(162,213)(163,212)(164,211)(165,215)(171,200)
(172,199)(173,198)(174,197)(175,196)(176,201)(177,205)(178,204)(179,203)
(180,202)(186,189)(187,188)(191,241)(192,245)(193,244)(194,243)(195,242)
(206,234)(207,233)(208,232)(209,231)(210,235)(217,220)(218,219)(246,250)
(247,249);
s1 := Sym(250)!(  2,  5)(  3,  4)(  6, 41)(  7, 45)(  8, 44)(  9, 43)( 10, 42)
( 11, 59)( 12, 58)( 13, 57)( 14, 56)( 15, 60)( 16,100)( 17, 99)( 18, 98)
( 19, 97)( 20, 96)( 21,114)( 22,113)( 23,112)( 24,111)( 25,115)( 26, 61)
( 27, 65)( 28, 64)( 29, 63)( 30, 62)( 31, 78)( 32, 77)( 33, 76)( 34, 80)
( 35, 79)( 36,118)( 37,117)( 38,116)( 39,120)( 40,119)( 46, 47)( 48, 50)
( 51,125)( 52,124)( 53,123)( 54,122)( 55,121)( 67, 70)( 68, 69)( 71, 84)
( 72, 83)( 73, 82)( 74, 81)( 75, 85)( 86, 88)( 89, 90)( 91,105)( 92,104)
( 93,103)( 94,102)( 95,101)(106,108)(109,110)(127,130)(128,129)(131,166)
(132,170)(133,169)(134,168)(135,167)(136,184)(137,183)(138,182)(139,181)
(140,185)(141,225)(142,224)(143,223)(144,222)(145,221)(146,239)(147,238)
(148,237)(149,236)(150,240)(151,186)(152,190)(153,189)(154,188)(155,187)
(156,203)(157,202)(158,201)(159,205)(160,204)(161,243)(162,242)(163,241)
(164,245)(165,244)(171,172)(173,175)(176,250)(177,249)(178,248)(179,247)
(180,246)(192,195)(193,194)(196,209)(197,208)(198,207)(199,206)(200,210)
(211,213)(214,215)(216,230)(217,229)(218,228)(219,227)(220,226)(231,233)
(234,235);
s2 := Sym(250)!(  1,216)(  2,217)(  3,218)(  4,219)(  5,220)(  6,213)(  7,214)
(  8,215)(  9,211)( 10,212)( 11,210)( 12,206)( 13,207)( 14,208)( 15,209)
( 16,202)( 17,203)( 18,204)( 19,205)( 20,201)( 21,224)( 22,225)( 23,221)
( 24,222)( 25,223)( 26,194)( 27,195)( 28,191)( 29,192)( 30,193)( 31,186)
( 32,187)( 33,188)( 34,189)( 35,190)( 36,183)( 37,184)( 38,185)( 39,181)
( 40,182)( 41,180)( 42,176)( 43,177)( 44,178)( 45,179)( 46,197)( 47,198)
( 48,199)( 49,200)( 50,196)( 51,167)( 52,168)( 53,169)( 54,170)( 55,166)
( 56,164)( 57,165)( 58,161)( 59,162)( 60,163)( 61,156)( 62,157)( 63,158)
( 64,159)( 65,160)( 66,153)( 67,154)( 68,155)( 69,151)( 70,152)( 71,175)
( 72,171)( 73,172)( 74,173)( 75,174)( 76,145)( 77,141)( 78,142)( 79,143)
( 80,144)( 81,137)( 82,138)( 83,139)( 84,140)( 85,136)( 86,134)( 87,135)
( 88,131)( 89,132)( 90,133)( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)
( 96,148)( 97,149)( 98,150)( 99,146)(100,147)(101,243)(102,244)(103,245)
(104,241)(105,242)(106,240)(107,236)(108,237)(109,238)(110,239)(111,232)
(112,233)(113,234)(114,235)(115,231)(116,229)(117,230)(118,226)(119,227)
(120,228)(121,246)(122,247)(123,248)(124,249)(125,250);
poly := sub<Sym(250)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
to this polytope