Polytope of Type {4,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,20}*2000a
if this polytope has a name.
Group : SmallGroup(2000,482)
Rank : 3
Schlafli Type : {4,20}
Number of vertices, edges, etc : 50, 500, 250
Order of s0s1s2 : 10
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,20}*1000
5-fold quotients : {4,4}*400
10-fold quotients : {4,4}*200
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)( 2,220)( 3,219)( 4,218)( 5,217)( 6,162)( 7,161)( 8,165)
( 9,164)( 10,163)( 11,235)( 12,234)( 13,233)( 14,232)( 15,231)( 16,180)
( 17,179)( 18,178)( 19,177)( 20,176)( 21,147)( 22,146)( 23,150)( 24,149)
( 25,148)( 26,243)( 27,242)( 28,241)( 29,245)( 30,244)( 31,189)( 32,188)
( 33,187)( 34,186)( 35,190)( 36,132)( 37,131)( 38,135)( 39,134)( 40,133)
( 41,202)( 42,201)( 43,205)( 44,204)( 45,203)( 46,174)( 47,173)( 48,172)
( 49,171)( 50,175)( 51,145)( 52,144)( 53,143)( 54,142)( 55,141)( 56,211)
( 57,215)( 58,214)( 59,213)( 60,212)( 61,159)( 62,158)( 63,157)( 64,156)
( 65,160)( 66,229)( 67,228)( 68,227)( 69,226)( 70,230)( 71,196)( 72,200)
( 73,199)( 74,198)( 75,197)( 76,167)( 77,166)( 78,170)( 79,169)( 80,168)
( 81,238)( 82,237)( 83,236)( 84,240)( 85,239)( 86,181)( 87,185)( 88,184)
( 89,183)( 90,182)( 91,126)( 92,130)( 93,129)( 94,128)( 95,127)( 96,223)
( 97,222)( 98,221)( 99,225)(100,224)(101,194)(102,193)(103,192)(104,191)
(105,195)(106,140)(107,139)(108,138)(109,137)(110,136)(111,208)(112,207)
(113,206)(114,210)(115,209)(116,153)(117,152)(118,151)(119,155)(120,154)
(121,250)(122,249)(123,248)(124,247)(125,246);;
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,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*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)( 2,220)( 3,219)( 4,218)( 5,217)( 6,162)( 7,161)
( 8,165)( 9,164)( 10,163)( 11,235)( 12,234)( 13,233)( 14,232)( 15,231)
( 16,180)( 17,179)( 18,178)( 19,177)( 20,176)( 21,147)( 22,146)( 23,150)
( 24,149)( 25,148)( 26,243)( 27,242)( 28,241)( 29,245)( 30,244)( 31,189)
( 32,188)( 33,187)( 34,186)( 35,190)( 36,132)( 37,131)( 38,135)( 39,134)
( 40,133)( 41,202)( 42,201)( 43,205)( 44,204)( 45,203)( 46,174)( 47,173)
( 48,172)( 49,171)( 50,175)( 51,145)( 52,144)( 53,143)( 54,142)( 55,141)
( 56,211)( 57,215)( 58,214)( 59,213)( 60,212)( 61,159)( 62,158)( 63,157)
( 64,156)( 65,160)( 66,229)( 67,228)( 68,227)( 69,226)( 70,230)( 71,196)
( 72,200)( 73,199)( 74,198)( 75,197)( 76,167)( 77,166)( 78,170)( 79,169)
( 80,168)( 81,238)( 82,237)( 83,236)( 84,240)( 85,239)( 86,181)( 87,185)
( 88,184)( 89,183)( 90,182)( 91,126)( 92,130)( 93,129)( 94,128)( 95,127)
( 96,223)( 97,222)( 98,221)( 99,225)(100,224)(101,194)(102,193)(103,192)
(104,191)(105,195)(106,140)(107,139)(108,138)(109,137)(110,136)(111,208)
(112,207)(113,206)(114,210)(115,209)(116,153)(117,152)(118,151)(119,155)
(120,154)(121,250)(122,249)(123,248)(124,247)(125,246);
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,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References : None.
to this polytope