Polytope of Type {2,50,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,50,10}*2000b
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) :
   2-fold quotients : {2,25,10}*1000
   5-fold quotients : {2,50,2}*400, {2,10,10}*400c
   10-fold quotients : {2,25,2}*200, {2,5,10}*200
   25-fold quotients : {2,10,2}*80
   50-fold quotients : {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)(  8, 23)(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 18)
( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 28,107)( 29,106)( 30,105)( 31,104)
( 32,103)( 33,127)( 34,126)( 35,125)( 36,124)( 37,123)( 38,122)( 39,121)
( 40,120)( 41,119)( 42,118)( 43,117)( 44,116)( 45,115)( 46,114)( 47,113)
( 48,112)( 49,111)( 50,110)( 51,109)( 52,108)( 53, 82)( 54, 81)( 55, 80)
( 56, 79)( 57, 78)( 58,102)( 59,101)( 60,100)( 61, 99)( 62, 98)( 63, 97)
( 64, 96)( 65, 95)( 66, 94)( 67, 93)( 68, 92)( 69, 91)( 70, 90)( 71, 89)
( 72, 88)( 73, 87)( 74, 86)( 75, 85)( 76, 84)( 77, 83)(129,132)(130,131)
(133,148)(134,152)(135,151)(136,150)(137,149)(138,143)(139,147)(140,146)
(141,145)(142,144)(153,232)(154,231)(155,230)(156,229)(157,228)(158,252)
(159,251)(160,250)(161,249)(162,248)(163,247)(164,246)(165,245)(166,244)
(167,243)(168,242)(169,241)(170,240)(171,239)(172,238)(173,237)(174,236)
(175,235)(176,234)(177,233)(178,207)(179,206)(180,205)(181,204)(182,203)
(183,227)(184,226)(185,225)(186,224)(187,223)(188,222)(189,221)(190,220)
(191,219)(192,218)(193,217)(194,216)(195,215)(196,214)(197,213)(198,212)
(199,211)(200,210)(201,209)(202,208);;
s2 := (  3,158)(  4,162)(  5,161)(  6,160)(  7,159)(  8,153)(  9,157)( 10,156)
( 11,155)( 12,154)( 13,173)( 14,177)( 15,176)( 16,175)( 17,174)( 18,168)
( 19,172)( 20,171)( 21,170)( 22,169)( 23,163)( 24,167)( 25,166)( 26,165)
( 27,164)( 28,133)( 29,137)( 30,136)( 31,135)( 32,134)( 33,128)( 34,132)
( 35,131)( 36,130)( 37,129)( 38,148)( 39,152)( 40,151)( 41,150)( 42,149)
( 43,143)( 44,147)( 45,146)( 46,145)( 47,144)( 48,138)( 49,142)( 50,141)
( 51,140)( 52,139)( 53,237)( 54,236)( 55,235)( 56,234)( 57,233)( 58,232)
( 59,231)( 60,230)( 61,229)( 62,228)( 63,252)( 64,251)( 65,250)( 66,249)
( 67,248)( 68,247)( 69,246)( 70,245)( 71,244)( 72,243)( 73,242)( 74,241)
( 75,240)( 76,239)( 77,238)( 78,212)( 79,211)( 80,210)( 81,209)( 82,208)
( 83,207)( 84,206)( 85,205)( 86,204)( 87,203)( 88,227)( 89,226)( 90,225)
( 91,224)( 92,223)( 93,222)( 94,221)( 95,220)( 96,219)( 97,218)( 98,217)
( 99,216)(100,215)(101,214)(102,213)(103,187)(104,186)(105,185)(106,184)
(107,183)(108,182)(109,181)(110,180)(111,179)(112,178)(113,202)(114,201)
(115,200)(116,199)(117,198)(118,197)(119,196)(120,195)(121,194)(122,193)
(123,192)(124,191)(125,190)(126,189)(127,188);;
s3 := (  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);;
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*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*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*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)(  8, 23)(  9, 27)( 10, 26)( 11, 25)( 12, 24)
( 13, 18)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 28,107)( 29,106)( 30,105)
( 31,104)( 32,103)( 33,127)( 34,126)( 35,125)( 36,124)( 37,123)( 38,122)
( 39,121)( 40,120)( 41,119)( 42,118)( 43,117)( 44,116)( 45,115)( 46,114)
( 47,113)( 48,112)( 49,111)( 50,110)( 51,109)( 52,108)( 53, 82)( 54, 81)
( 55, 80)( 56, 79)( 57, 78)( 58,102)( 59,101)( 60,100)( 61, 99)( 62, 98)
( 63, 97)( 64, 96)( 65, 95)( 66, 94)( 67, 93)( 68, 92)( 69, 91)( 70, 90)
( 71, 89)( 72, 88)( 73, 87)( 74, 86)( 75, 85)( 76, 84)( 77, 83)(129,132)
(130,131)(133,148)(134,152)(135,151)(136,150)(137,149)(138,143)(139,147)
(140,146)(141,145)(142,144)(153,232)(154,231)(155,230)(156,229)(157,228)
(158,252)(159,251)(160,250)(161,249)(162,248)(163,247)(164,246)(165,245)
(166,244)(167,243)(168,242)(169,241)(170,240)(171,239)(172,238)(173,237)
(174,236)(175,235)(176,234)(177,233)(178,207)(179,206)(180,205)(181,204)
(182,203)(183,227)(184,226)(185,225)(186,224)(187,223)(188,222)(189,221)
(190,220)(191,219)(192,218)(193,217)(194,216)(195,215)(196,214)(197,213)
(198,212)(199,211)(200,210)(201,209)(202,208);
s2 := Sym(252)!(  3,158)(  4,162)(  5,161)(  6,160)(  7,159)(  8,153)(  9,157)
( 10,156)( 11,155)( 12,154)( 13,173)( 14,177)( 15,176)( 16,175)( 17,174)
( 18,168)( 19,172)( 20,171)( 21,170)( 22,169)( 23,163)( 24,167)( 25,166)
( 26,165)( 27,164)( 28,133)( 29,137)( 30,136)( 31,135)( 32,134)( 33,128)
( 34,132)( 35,131)( 36,130)( 37,129)( 38,148)( 39,152)( 40,151)( 41,150)
( 42,149)( 43,143)( 44,147)( 45,146)( 46,145)( 47,144)( 48,138)( 49,142)
( 50,141)( 51,140)( 52,139)( 53,237)( 54,236)( 55,235)( 56,234)( 57,233)
( 58,232)( 59,231)( 60,230)( 61,229)( 62,228)( 63,252)( 64,251)( 65,250)
( 66,249)( 67,248)( 68,247)( 69,246)( 70,245)( 71,244)( 72,243)( 73,242)
( 74,241)( 75,240)( 76,239)( 77,238)( 78,212)( 79,211)( 80,210)( 81,209)
( 82,208)( 83,207)( 84,206)( 85,205)( 86,204)( 87,203)( 88,227)( 89,226)
( 90,225)( 91,224)( 92,223)( 93,222)( 94,221)( 95,220)( 96,219)( 97,218)
( 98,217)( 99,216)(100,215)(101,214)(102,213)(103,187)(104,186)(105,185)
(106,184)(107,183)(108,182)(109,181)(110,180)(111,179)(112,178)(113,202)
(114,201)(115,200)(116,199)(117,198)(118,197)(119,196)(120,195)(121,194)
(122,193)(123,192)(124,191)(125,190)(126,189)(127,188);
s3 := 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);
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*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope