Polytope of Type {2,50,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,50,10}*2000a
if this polytope has a name.
Group : SmallGroup(2000,500)
Rank : 4
Schlafli Type : {2,50,10}
Number of vertices, edges, etc : 2, 50, 250, 10
Order of s₀s₁s₂s₃ : 50
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,50,2}*400, {2,10,10}*400a
   10-fold quotients : {2,25,2}*200
   25-fold quotients : {2,2,10}*80, {2,10,2}*80
   50-fold quotients : {2,2,5}*40, {2,5,2}*40
   125-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 28,107)( 29,106)( 30,105)( 31,104)( 32,103)( 33,112)
( 34,111)( 35,110)( 36,109)( 37,108)( 38,117)( 39,116)( 40,115)( 41,114)
( 42,113)( 43,122)( 44,121)( 45,120)( 46,119)( 47,118)( 48,127)( 49,126)
( 50,125)( 51,124)( 52,123)( 53, 82)( 54, 81)( 55, 80)( 56, 79)( 57, 78)
( 58, 87)( 59, 86)( 60, 85)( 61, 84)( 62, 83)( 63, 92)( 64, 91)( 65, 90)
( 66, 89)( 67, 88)( 68, 97)( 69, 96)( 70, 95)( 71, 94)( 72, 93)( 73,102)
( 74,101)( 75,100)( 76, 99)( 77, 98)(129,132)(130,131)(134,137)(135,136)
(139,142)(140,141)(144,147)(145,146)(149,152)(150,151)(153,232)(154,231)
(155,230)(156,229)(157,228)(158,237)(159,236)(160,235)(161,234)(162,233)
(163,242)(164,241)(165,240)(166,239)(167,238)(168,247)(169,246)(170,245)
(171,244)(172,243)(173,252)(174,251)(175,250)(176,249)(177,248)(178,207)
(179,206)(180,205)(181,204)(182,203)(183,212)(184,211)(185,210)(186,209)
(187,208)(188,217)(189,216)(190,215)(191,214)(192,213)(193,222)(194,221)
(195,220)(196,219)(197,218)(198,227)(199,226)(200,225)(201,224)(202,223);;
s2 := (  3, 28)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 48)(  9, 52)( 10, 51)
( 11, 50)( 12, 49)( 13, 43)( 14, 47)( 15, 46)( 16, 45)( 17, 44)( 18, 38)
( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 33)( 24, 37)( 25, 36)( 26, 35)
( 27, 34)( 53,107)( 54,106)( 55,105)( 56,104)( 57,103)( 58,127)( 59,126)
( 60,125)( 61,124)( 62,123)( 63,122)( 64,121)( 65,120)( 66,119)( 67,118)
( 68,117)( 69,116)( 70,115)( 71,114)( 72,113)( 73,112)( 74,111)( 75,110)
( 76,109)( 77,108)( 78, 82)( 79, 81)( 83,102)( 84,101)( 85,100)( 86, 99)
( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 92, 93)(128,153)(129,157)
(130,156)(131,155)(132,154)(133,173)(134,177)(135,176)(136,175)(137,174)
(138,168)(139,172)(140,171)(141,170)(142,169)(143,163)(144,167)(145,166)
(146,165)(147,164)(148,158)(149,162)(150,161)(151,160)(152,159)(178,232)
(179,231)(180,230)(181,229)(182,228)(183,252)(184,251)(185,250)(186,249)
(187,248)(188,247)(189,246)(190,245)(191,244)(192,243)(193,242)(194,241)
(195,240)(196,239)(197,238)(198,237)(199,236)(200,235)(201,234)(202,233)
(203,207)(204,206)(208,227)(209,226)(210,225)(211,224)(212,223)(213,222)
(214,221)(215,220)(216,219)(217,218);;
s3 := (  3,133)(  4,134)(  5,135)(  6,136)(  7,137)(  8,128)(  9,129)( 10,130)
( 11,131)( 12,132)( 13,148)( 14,149)( 15,150)( 16,151)( 17,152)( 18,143)
( 19,144)( 20,145)( 21,146)( 22,147)( 23,138)( 24,139)( 25,140)( 26,141)
( 27,142)( 28,158)( 29,159)( 30,160)( 31,161)( 32,162)( 33,153)( 34,154)
( 35,155)( 36,156)( 37,157)( 38,173)( 39,174)( 40,175)( 41,176)( 42,177)
( 43,168)( 44,169)( 45,170)( 46,171)( 47,172)( 48,163)( 49,164)( 50,165)
( 51,166)( 52,167)( 53,183)( 54,184)( 55,185)( 56,186)( 57,187)( 58,178)
( 59,179)( 60,180)( 61,181)( 62,182)( 63,198)( 64,199)( 65,200)( 66,201)
( 67,202)( 68,193)( 69,194)( 70,195)( 71,196)( 72,197)( 73,188)( 74,189)
( 75,190)( 76,191)( 77,192)( 78,208)( 79,209)( 80,210)( 81,211)( 82,212)
( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,223)( 89,224)( 90,225)
( 91,226)( 92,227)( 93,218)( 94,219)( 95,220)( 96,221)( 97,222)( 98,213)
( 99,214)(100,215)(101,216)(102,217)(103,233)(104,234)(105,235)(106,236)
(107,237)(108,228)(109,229)(110,230)(111,231)(112,232)(113,248)(114,249)
(115,250)(116,251)(117,252)(118,243)(119,244)(120,245)(121,246)(122,247)
(123,238)(124,239)(125,240)(126,241)(127,242);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(252)!(1,2);
s1 := Sym(252)!(  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 28,107)( 29,106)( 30,105)( 31,104)( 32,103)
( 33,112)( 34,111)( 35,110)( 36,109)( 37,108)( 38,117)( 39,116)( 40,115)
( 41,114)( 42,113)( 43,122)( 44,121)( 45,120)( 46,119)( 47,118)( 48,127)
( 49,126)( 50,125)( 51,124)( 52,123)( 53, 82)( 54, 81)( 55, 80)( 56, 79)
( 57, 78)( 58, 87)( 59, 86)( 60, 85)( 61, 84)( 62, 83)( 63, 92)( 64, 91)
( 65, 90)( 66, 89)( 67, 88)( 68, 97)( 69, 96)( 70, 95)( 71, 94)( 72, 93)
( 73,102)( 74,101)( 75,100)( 76, 99)( 77, 98)(129,132)(130,131)(134,137)
(135,136)(139,142)(140,141)(144,147)(145,146)(149,152)(150,151)(153,232)
(154,231)(155,230)(156,229)(157,228)(158,237)(159,236)(160,235)(161,234)
(162,233)(163,242)(164,241)(165,240)(166,239)(167,238)(168,247)(169,246)
(170,245)(171,244)(172,243)(173,252)(174,251)(175,250)(176,249)(177,248)
(178,207)(179,206)(180,205)(181,204)(182,203)(183,212)(184,211)(185,210)
(186,209)(187,208)(188,217)(189,216)(190,215)(191,214)(192,213)(193,222)
(194,221)(195,220)(196,219)(197,218)(198,227)(199,226)(200,225)(201,224)
(202,223);
s2 := Sym(252)!(  3, 28)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 48)(  9, 52)
( 10, 51)( 11, 50)( 12, 49)( 13, 43)( 14, 47)( 15, 46)( 16, 45)( 17, 44)
( 18, 38)( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 33)( 24, 37)( 25, 36)
( 26, 35)( 27, 34)( 53,107)( 54,106)( 55,105)( 56,104)( 57,103)( 58,127)
( 59,126)( 60,125)( 61,124)( 62,123)( 63,122)( 64,121)( 65,120)( 66,119)
( 67,118)( 68,117)( 69,116)( 70,115)( 71,114)( 72,113)( 73,112)( 74,111)
( 75,110)( 76,109)( 77,108)( 78, 82)( 79, 81)( 83,102)( 84,101)( 85,100)
( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 92, 93)(128,153)
(129,157)(130,156)(131,155)(132,154)(133,173)(134,177)(135,176)(136,175)
(137,174)(138,168)(139,172)(140,171)(141,170)(142,169)(143,163)(144,167)
(145,166)(146,165)(147,164)(148,158)(149,162)(150,161)(151,160)(152,159)
(178,232)(179,231)(180,230)(181,229)(182,228)(183,252)(184,251)(185,250)
(186,249)(187,248)(188,247)(189,246)(190,245)(191,244)(192,243)(193,242)
(194,241)(195,240)(196,239)(197,238)(198,237)(199,236)(200,235)(201,234)
(202,233)(203,207)(204,206)(208,227)(209,226)(210,225)(211,224)(212,223)
(213,222)(214,221)(215,220)(216,219)(217,218);
s3 := Sym(252)!(  3,133)(  4,134)(  5,135)(  6,136)(  7,137)(  8,128)(  9,129)
( 10,130)( 11,131)( 12,132)( 13,148)( 14,149)( 15,150)( 16,151)( 17,152)
( 18,143)( 19,144)( 20,145)( 21,146)( 22,147)( 23,138)( 24,139)( 25,140)
( 26,141)( 27,142)( 28,158)( 29,159)( 30,160)( 31,161)( 32,162)( 33,153)
( 34,154)( 35,155)( 36,156)( 37,157)( 38,173)( 39,174)( 40,175)( 41,176)
( 42,177)( 43,168)( 44,169)( 45,170)( 46,171)( 47,172)( 48,163)( 49,164)
( 50,165)( 51,166)( 52,167)( 53,183)( 54,184)( 55,185)( 56,186)( 57,187)
( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,198)( 64,199)( 65,200)
( 66,201)( 67,202)( 68,193)( 69,194)( 70,195)( 71,196)( 72,197)( 73,188)
( 74,189)( 75,190)( 76,191)( 77,192)( 78,208)( 79,209)( 80,210)( 81,211)
( 82,212)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,223)( 89,224)
( 90,225)( 91,226)( 92,227)( 93,218)( 94,219)( 95,220)( 96,221)( 97,222)
( 98,213)( 99,214)(100,215)(101,216)(102,217)(103,233)(104,234)(105,235)
(106,236)(107,237)(108,228)(109,229)(110,230)(111,231)(112,232)(113,248)
(114,249)(115,250)(116,251)(117,252)(118,243)(119,244)(120,245)(121,246)
(122,247)(123,238)(124,239)(125,240)(126,241)(127,242);
poly := sub<Sym(252)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope