Polytope of Type {10,10,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10,10}*2000f
if this polytope has a name.
Group : SmallGroup(2000,946)
Rank : 4
Schlafli Type : {10,10,10}
Number of vertices, edges, etc : 10, 50, 50, 10
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
   Self-Dual
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 : {10,5,10}*1000
   5-fold quotients : {2,10,10}*400c, {10,10,2}*400b
   10-fold quotients : {2,5,10}*200, {10,5,2}*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.
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

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

References : None.
to this polytope