Polytope of Type {50,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {50,10}*1000b
if this polytope has a name.
Group : SmallGroup(1000,105)
Rank : 3
Schlafli Type : {50,10}
Number of vertices, edges, etc : 50, 250, 10
Order of s₀s₁s₂ : 50
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {50,10,2} of size 2000
Vertex Figure Of :
   {2,50,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {25,10}*500
   5-fold quotients : {50,2}*200, {10,10}*200c
   10-fold quotients : {25,2}*100, {5,10}*100
   25-fold quotients : {10,2}*40
   50-fold quotients : {5,2}*20
   125-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {100,10}*2000b, {50,20}*2000b
Permutation Representation (GAP) :

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