Polytope of Type {2,10,50}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,50}*2000b
if this polytope has a name.
Group : SmallGroup(2000,500)
Rank : 4
Schlafli Type : {2,10,50}
Number of vertices, edges, etc : 2, 10, 250, 50
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) :
   2-fold quotients : {2,10,25}*1000
   5-fold quotients : {2,2,50}*400, {2,10,10}*400b
   10-fold quotients : {2,2,25}*200, {2,10,5}*200
   25-fold quotients : {2,2,10}*80
   50-fold quotients : {2,2,5}*40
   125-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope