Polytope of Type {2,10,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,10}*2000a
if this polytope has a name.
Group : SmallGroup(2000,501)
Rank : 4
Schlafli Type : {2,10,10}
Number of vertices, edges, etc : 2, 50, 250, 50
Order of s₀s₁s₂s₃ : 10
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 : {2,5,10}*1000
   5-fold quotients : {2,10,10}*400c
   10-fold quotients : {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 := (  8, 23)(  9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 18)( 14, 19)( 15, 20)( 16, 21)( 17, 22)( 28,103)( 29,104)( 30,105)( 31,106)( 32,107)( 33,123)( 34,124)( 35,125)( 36,126)( 37,127)( 38,118)( 39,119)( 40,120)( 41,121)( 42,122)( 43,113)( 44,114)( 45,115)( 46,116)( 47,117)( 48,108)( 49,109)( 50,110)( 51,111)( 52,112)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)( 58, 98)( 59, 99)( 60,100)( 61,101)( 62,102)( 63, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68, 88)( 69, 89)( 70, 90)( 71, 91)( 72, 92)( 73, 83)( 74, 84)( 75, 85)( 76, 86)( 77, 87)(133,148)(134,149)(135,150)(136,151)(137,152)(138,143)(139,144)(140,145)(141,146)(142,147)(153,228)(154,229)(155,230)(156,231)(157,232)(158,248)(159,249)(160,250)(161,251)(162,252)(163,243)(164,244)(165,245)(166,246)(167,247)(168,238)(169,239)(170,240)(171,241)(172,242)(173,233)(174,234)(175,235)(176,236)(177,237)(178,203)(179,204)(180,205)(181,206)(182,207)(183,223)(184,224)(185,225)(186,226)(187,227)(188,218)(189,219)(190,220)(191,221)(192,222)(193,213)(194,214)(195,215)(196,216)(197,217)(198,208)(199,209)(200,210)(201,211)(202,212);;
s2 := (  3,184)(  4,185)(  5,186)(  6,187)(  7,183)(  8,182)(  9,178)( 10,179)( 11,180)( 12,181)( 13,200)( 14,201)( 15,202)( 16,198)( 17,199)( 18,193)( 19,194)( 20,195)( 21,196)( 22,197)( 23,191)( 24,192)( 25,188)( 26,189)( 27,190)( 28,159)( 29,160)( 30,161)( 31,162)( 32,158)( 33,157)( 34,153)( 35,154)( 36,155)( 37,156)( 38,175)( 39,176)( 40,177)( 41,173)( 42,174)( 43,168)( 44,169)( 45,170)( 46,171)( 47,172)( 48,166)( 49,167)( 50,163)( 51,164)( 52,165)( 53,134)( 54,135)( 55,136)( 56,137)( 57,133)( 58,132)( 59,128)( 60,129)( 61,130)( 62,131)( 63,150)( 64,151)( 65,152)( 66,148)( 67,149)( 68,143)( 69,144)( 70,145)( 71,146)( 72,147)( 73,141)( 74,142)( 75,138)( 76,139)( 77,140)( 78,234)( 79,235)( 80,236)( 81,237)( 82,233)( 83,232)( 84,228)( 85,229)( 86,230)( 87,231)( 88,250)( 89,251)( 90,252)( 91,248)( 92,249)( 93,243)( 94,244)( 95,245)( 96,246)( 97,247)( 98,241)( 99,242)(100,238)(101,239)(102,240)(103,209)(104,210)(105,211)(106,212)(107,208)(108,207)(109,203)(110,204)(111,205)(112,206)(113,225)(114,226)(115,227)(116,223)(117,224)(118,218)(119,219)(120,220)(121,221)(122,222)(123,216)(124,217)(125,213)(126,214)(127,215);;
s3 := (  4,  7)(  5,  6)(  8, 23)(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 18)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 29, 32)( 30, 31)( 33, 48)( 34, 52)( 35, 51)( 36, 50)( 37, 49)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 54, 57)( 55, 56)( 58, 73)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 68)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 79, 82)( 80, 81)( 83, 98)( 84,102)( 85,101)( 86,100)( 87, 99)( 88, 93)( 89, 97)( 90, 96)( 91, 95)( 92, 94)(104,107)(105,106)(108,123)(109,127)(110,126)(111,125)(112,124)(113,118)(114,122)(115,121)(116,120)(117,119)(129,132)(130,131)(133,148)(134,152)(135,151)(136,150)(137,149)(138,143)(139,147)(140,146)(141,145)(142,144)(154,157)(155,156)(158,173)(159,177)(160,176)(161,175)(162,174)(163,168)(164,172)(165,171)(166,170)(167,169)(179,182)(180,181)(183,198)(184,202)(185,201)(186,200)(187,199)(188,193)(189,197)(190,196)(191,195)(192,194)(204,207)(205,206)(208,223)(209,227)(210,226)(211,225)(212,224)(213,218)(214,222)(215,221)(216,220)(217,219)(229,232)(230,231)(233,248)(234,252)(235,251)(236,250)(237,249)(238,243)(239,247)(240,246)(241,245)(242,244);;
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*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2 ];;
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)( 28,103)( 29,104)( 30,105)( 31,106)( 32,107)( 33,123)( 34,124)( 35,125)( 36,126)( 37,127)( 38,118)( 39,119)( 40,120)( 41,121)( 42,122)( 43,113)( 44,114)( 45,115)( 46,116)( 47,117)( 48,108)( 49,109)( 50,110)( 51,111)( 52,112)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)( 58, 98)( 59, 99)( 60,100)( 61,101)( 62,102)( 63, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68, 88)( 69, 89)( 70, 90)( 71, 91)( 72, 92)( 73, 83)( 74, 84)( 75, 85)( 76, 86)( 77, 87)(133,148)(134,149)(135,150)(136,151)(137,152)(138,143)(139,144)(140,145)(141,146)(142,147)(153,228)(154,229)(155,230)(156,231)(157,232)(158,248)(159,249)(160,250)(161,251)(162,252)(163,243)(164,244)(165,245)(166,246)(167,247)(168,238)(169,239)(170,240)(171,241)(172,242)(173,233)(174,234)(175,235)(176,236)(177,237)(178,203)(179,204)(180,205)(181,206)(182,207)(183,223)(184,224)(185,225)(186,226)(187,227)(188,218)(189,219)(190,220)(191,221)(192,222)(193,213)(194,214)(195,215)(196,216)(197,217)(198,208)(199,209)(200,210)(201,211)(202,212);
s2 := Sym(252)!(  3,184)(  4,185)(  5,186)(  6,187)(  7,183)(  8,182)(  9,178)( 10,179)( 11,180)( 12,181)( 13,200)( 14,201)( 15,202)( 16,198)( 17,199)( 18,193)( 19,194)( 20,195)( 21,196)( 22,197)( 23,191)( 24,192)( 25,188)( 26,189)( 27,190)( 28,159)( 29,160)( 30,161)( 31,162)( 32,158)( 33,157)( 34,153)( 35,154)( 36,155)( 37,156)( 38,175)( 39,176)( 40,177)( 41,173)( 42,174)( 43,168)( 44,169)( 45,170)( 46,171)( 47,172)( 48,166)( 49,167)( 50,163)( 51,164)( 52,165)( 53,134)( 54,135)( 55,136)( 56,137)( 57,133)( 58,132)( 59,128)( 60,129)( 61,130)( 62,131)( 63,150)( 64,151)( 65,152)( 66,148)( 67,149)( 68,143)( 69,144)( 70,145)( 71,146)( 72,147)( 73,141)( 74,142)( 75,138)( 76,139)( 77,140)( 78,234)( 79,235)( 80,236)( 81,237)( 82,233)( 83,232)( 84,228)( 85,229)( 86,230)( 87,231)( 88,250)( 89,251)( 90,252)( 91,248)( 92,249)( 93,243)( 94,244)( 95,245)( 96,246)( 97,247)( 98,241)( 99,242)(100,238)(101,239)(102,240)(103,209)(104,210)(105,211)(106,212)(107,208)(108,207)(109,203)(110,204)(111,205)(112,206)(113,225)(114,226)(115,227)(116,223)(117,224)(118,218)(119,219)(120,220)(121,221)(122,222)(123,216)(124,217)(125,213)(126,214)(127,215);
s3 := 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)( 29, 32)( 30, 31)( 33, 48)( 34, 52)( 35, 51)( 36, 50)( 37, 49)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 54, 57)( 55, 56)( 58, 73)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 68)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 79, 82)( 80, 81)( 83, 98)( 84,102)( 85,101)( 86,100)( 87, 99)( 88, 93)( 89, 97)( 90, 96)( 91, 95)( 92, 94)(104,107)(105,106)(108,123)(109,127)(110,126)(111,125)(112,124)(113,118)(114,122)(115,121)(116,120)(117,119)(129,132)(130,131)(133,148)(134,152)(135,151)(136,150)(137,149)(138,143)(139,147)(140,146)(141,145)(142,144)(154,157)(155,156)(158,173)(159,177)(160,176)(161,175)(162,174)(163,168)(164,172)(165,171)(166,170)(167,169)(179,182)(180,181)(183,198)(184,202)(185,201)(186,200)(187,199)(188,193)(189,197)(190,196)(191,195)(192,194)(204,207)(205,206)(208,223)(209,227)(210,226)(211,225)(212,224)(213,218)(214,222)(215,221)(216,220)(217,219)(229,232)(230,231)(233,248)(234,252)(235,251)(236,250)(237,249)(238,243)(239,247)(240,246)(241,245)(242,244);
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*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2 >;

to this polytope