Polytope of Type {50,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {50,10}*1000a
Also Known As : {50,10|2}. if this polytope has another 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 : 2
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) :
   5-fold quotients : {50,2}*200, {10,10}*200a
   10-fold quotients : {25,2}*100
   25-fold quotients : {2,10}*40, {10,2}*40
   50-fold quotients : {2,5}*20, {5,2}*20
   125-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {50,20}*2000a, {100,10}*2000a
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

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

Polytope of Type {50,10}

Twisty Puzzle