Polytope of Type {10,10,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10,5}*1000a
if this polytope has a name.
Group : SmallGroup(1000,106)
Rank : 4
Schlafli Type : {10,10,5}
Number of vertices, edges, etc : 10, 50, 25, 5
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 10
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,10,5,2} of size 2000
Vertex Figure Of :
   {2,10,10,5} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,10,5}*500
   5-fold quotients : {10,2,5}*200
   10-fold quotients : {5,2,5}*100
   25-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,10,5}*2000a, {10,10,10}*2000a
Permutation Representation (GAP) : 
s0 := (  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)
( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)
( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)
( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)
( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)
(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)
(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)(132,150)
(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)
(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)(161,166)
(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)(182,200)
(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)(190,192)
(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)(211,216)
(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)(232,250)
(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)(240,242);;
s1 := (  1,131)(  2,135)(  3,134)(  4,133)(  5,132)(  6,126)(  7,130)(  8,129)
(  9,128)( 10,127)( 11,146)( 12,150)( 13,149)( 14,148)( 15,147)( 16,141)
( 17,145)( 18,144)( 19,143)( 20,142)( 21,136)( 22,140)( 23,139)( 24,138)
( 25,137)( 26,156)( 27,160)( 28,159)( 29,158)( 30,157)( 31,151)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,171)( 37,175)( 38,174)( 39,173)( 40,172)
( 41,166)( 42,170)( 43,169)( 44,168)( 45,167)( 46,161)( 47,165)( 48,164)
( 49,163)( 50,162)( 51,181)( 52,185)( 53,184)( 54,183)( 55,182)( 56,176)
( 57,180)( 58,179)( 59,178)( 60,177)( 61,196)( 62,200)( 63,199)( 64,198)
( 65,197)( 66,191)( 67,195)( 68,194)( 69,193)( 70,192)( 71,186)( 72,190)
( 73,189)( 74,188)( 75,187)( 76,206)( 77,210)( 78,209)( 79,208)( 80,207)
( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,221)( 87,225)( 88,224)
( 89,223)( 90,222)( 91,216)( 92,220)( 93,219)( 94,218)( 95,217)( 96,211)
( 97,215)( 98,214)( 99,213)(100,212)(101,231)(102,235)(103,234)(104,233)
(105,232)(106,226)(107,230)(108,229)(109,228)(110,227)(111,246)(112,250)
(113,249)(114,248)(115,247)(116,241)(117,245)(118,244)(119,243)(120,242)
(121,236)(122,240)(123,239)(124,238)(125,237);;
s2 := (  1, 26)(  2, 30)(  3, 29)(  4, 28)(  5, 27)(  6, 32)(  7, 31)(  8, 35)
(  9, 34)( 10, 33)( 11, 38)( 12, 37)( 13, 36)( 14, 40)( 15, 39)( 16, 44)
( 17, 43)( 18, 42)( 19, 41)( 20, 45)( 21, 50)( 22, 49)( 23, 48)( 24, 47)
( 25, 46)( 51,101)( 52,105)( 53,104)( 54,103)( 55,102)( 56,107)( 57,106)
( 58,110)( 59,109)( 60,108)( 61,113)( 62,112)( 63,111)( 64,115)( 65,114)
( 66,119)( 67,118)( 68,117)( 69,116)( 70,120)( 71,125)( 72,124)( 73,123)
( 74,122)( 75,121)( 77, 80)( 78, 79)( 81, 82)( 83, 85)( 86, 88)( 89, 90)
( 91, 94)( 92, 93)( 96,100)( 97, 99)(126,151)(127,155)(128,154)(129,153)
(130,152)(131,157)(132,156)(133,160)(134,159)(135,158)(136,163)(137,162)
(138,161)(139,165)(140,164)(141,169)(142,168)(143,167)(144,166)(145,170)
(146,175)(147,174)(148,173)(149,172)(150,171)(176,226)(177,230)(178,229)
(179,228)(180,227)(181,232)(182,231)(183,235)(184,234)(185,233)(186,238)
(187,237)(188,236)(189,240)(190,239)(191,244)(192,243)(193,242)(194,241)
(195,245)(196,250)(197,249)(198,248)(199,247)(200,246)(202,205)(203,204)
(206,207)(208,210)(211,213)(214,215)(216,219)(217,218)(221,225)(222,224);;
s3 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31,106)
( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)( 39,113)
( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,121)( 47,125)
( 48,124)( 49,123)( 50,122)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)
( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)( 63, 89)
( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 96)
( 72,100)( 73, 99)( 74, 98)( 75, 97)(127,130)(128,129)(132,135)(133,134)
(137,140)(138,139)(142,145)(143,144)(147,150)(148,149)(151,226)(152,230)
(153,229)(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)(160,232)
(161,236)(162,240)(163,239)(164,238)(165,237)(166,241)(167,245)(168,244)
(169,243)(170,242)(171,246)(172,250)(173,249)(174,248)(175,247)(176,201)
(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)(183,209)(184,208)
(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)(191,216)(192,220)
(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)(199,223)(200,222);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(250)!(  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)
( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)
( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)
( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)
( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)
( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)
( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)
(111,116)(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)
(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)
(140,142)(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)
(161,166)(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)
(182,200)(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)
(190,192)(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)
(211,216)(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)
(232,250)(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)
(240,242);
s1 := Sym(250)!(  1,131)(  2,135)(  3,134)(  4,133)(  5,132)(  6,126)(  7,130)
(  8,129)(  9,128)( 10,127)( 11,146)( 12,150)( 13,149)( 14,148)( 15,147)
( 16,141)( 17,145)( 18,144)( 19,143)( 20,142)( 21,136)( 22,140)( 23,139)
( 24,138)( 25,137)( 26,156)( 27,160)( 28,159)( 29,158)( 30,157)( 31,151)
( 32,155)( 33,154)( 34,153)( 35,152)( 36,171)( 37,175)( 38,174)( 39,173)
( 40,172)( 41,166)( 42,170)( 43,169)( 44,168)( 45,167)( 46,161)( 47,165)
( 48,164)( 49,163)( 50,162)( 51,181)( 52,185)( 53,184)( 54,183)( 55,182)
( 56,176)( 57,180)( 58,179)( 59,178)( 60,177)( 61,196)( 62,200)( 63,199)
( 64,198)( 65,197)( 66,191)( 67,195)( 68,194)( 69,193)( 70,192)( 71,186)
( 72,190)( 73,189)( 74,188)( 75,187)( 76,206)( 77,210)( 78,209)( 79,208)
( 80,207)( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,221)( 87,225)
( 88,224)( 89,223)( 90,222)( 91,216)( 92,220)( 93,219)( 94,218)( 95,217)
( 96,211)( 97,215)( 98,214)( 99,213)(100,212)(101,231)(102,235)(103,234)
(104,233)(105,232)(106,226)(107,230)(108,229)(109,228)(110,227)(111,246)
(112,250)(113,249)(114,248)(115,247)(116,241)(117,245)(118,244)(119,243)
(120,242)(121,236)(122,240)(123,239)(124,238)(125,237);
s2 := Sym(250)!(  1, 26)(  2, 30)(  3, 29)(  4, 28)(  5, 27)(  6, 32)(  7, 31)
(  8, 35)(  9, 34)( 10, 33)( 11, 38)( 12, 37)( 13, 36)( 14, 40)( 15, 39)
( 16, 44)( 17, 43)( 18, 42)( 19, 41)( 20, 45)( 21, 50)( 22, 49)( 23, 48)
( 24, 47)( 25, 46)( 51,101)( 52,105)( 53,104)( 54,103)( 55,102)( 56,107)
( 57,106)( 58,110)( 59,109)( 60,108)( 61,113)( 62,112)( 63,111)( 64,115)
( 65,114)( 66,119)( 67,118)( 68,117)( 69,116)( 70,120)( 71,125)( 72,124)
( 73,123)( 74,122)( 75,121)( 77, 80)( 78, 79)( 81, 82)( 83, 85)( 86, 88)
( 89, 90)( 91, 94)( 92, 93)( 96,100)( 97, 99)(126,151)(127,155)(128,154)
(129,153)(130,152)(131,157)(132,156)(133,160)(134,159)(135,158)(136,163)
(137,162)(138,161)(139,165)(140,164)(141,169)(142,168)(143,167)(144,166)
(145,170)(146,175)(147,174)(148,173)(149,172)(150,171)(176,226)(177,230)
(178,229)(179,228)(180,227)(181,232)(182,231)(183,235)(184,234)(185,233)
(186,238)(187,237)(188,236)(189,240)(190,239)(191,244)(192,243)(193,242)
(194,241)(195,245)(196,250)(197,249)(198,248)(199,247)(200,246)(202,205)
(203,204)(206,207)(208,210)(211,213)(214,215)(216,219)(217,218)(221,225)
(222,224);
s3 := Sym(250)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)
( 31,106)( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)
( 39,113)( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,121)
( 47,125)( 48,124)( 49,123)( 50,122)( 51, 76)( 52, 80)( 53, 79)( 54, 78)
( 55, 77)( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)
( 63, 89)( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)
( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)(127,130)(128,129)(132,135)
(133,134)(137,140)(138,139)(142,145)(143,144)(147,150)(148,149)(151,226)
(152,230)(153,229)(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)
(160,232)(161,236)(162,240)(163,239)(164,238)(165,237)(166,241)(167,245)
(168,244)(169,243)(170,242)(171,246)(172,250)(173,249)(174,248)(175,247)
(176,201)(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)(183,209)
(184,208)(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)(191,216)
(192,220)(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)(199,223)
(200,222);
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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope