Polytope of Type {10,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,20}*2000f
if this polytope has a name.
Group : SmallGroup(2000,482)
Rank : 3
Schlafli Type : {10,20}
Number of vertices, edges, etc : 50, 500, 100
Order of s₀s₁s₂ : 4
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 : {10,20}*1000b
   5-fold quotients : {10,4}*400
   10-fold quotients : {10,4}*200
   125-fold quotients : {2,4}*16
   250-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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