Polytope of Type {2,10,10,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,10,5}*2000a
if this polytope has a name.
Group : SmallGroup(2000,501)
Rank : 5
Schlafli Type : {2,10,10,5}
Number of vertices, edges, etc : 2, 10, 50, 25, 5
Order of s0s1s2s3s4 : 10
Order of s0s1s2s3s4s3s2s1 : 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 : {2,5,10,5}*1000
   5-fold quotients : {2,10,2,5}*400
   10-fold quotients : {2,5,2,5}*200
   25-fold quotients : {2,2,2,5}*80
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)( 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);;
s2 := (  3,133)(  4,137)(  5,136)(  6,135)(  7,134)(  8,128)(  9,132)( 10,131)
( 11,130)( 12,129)( 13,148)( 14,152)( 15,151)( 16,150)( 17,149)( 18,143)
( 19,147)( 20,146)( 21,145)( 22,144)( 23,138)( 24,142)( 25,141)( 26,140)
( 27,139)( 28,158)( 29,162)( 30,161)( 31,160)( 32,159)( 33,153)( 34,157)
( 35,156)( 36,155)( 37,154)( 38,173)( 39,177)( 40,176)( 41,175)( 42,174)
( 43,168)( 44,172)( 45,171)( 46,170)( 47,169)( 48,163)( 49,167)( 50,166)
( 51,165)( 52,164)( 53,183)( 54,187)( 55,186)( 56,185)( 57,184)( 58,178)
( 59,182)( 60,181)( 61,180)( 62,179)( 63,198)( 64,202)( 65,201)( 66,200)
( 67,199)( 68,193)( 69,197)( 70,196)( 71,195)( 72,194)( 73,188)( 74,192)
( 75,191)( 76,190)( 77,189)( 78,208)( 79,212)( 80,211)( 81,210)( 82,209)
( 83,203)( 84,207)( 85,206)( 86,205)( 87,204)( 88,223)( 89,227)( 90,226)
( 91,225)( 92,224)( 93,218)( 94,222)( 95,221)( 96,220)( 97,219)( 98,213)
( 99,217)(100,216)(101,215)(102,214)(103,233)(104,237)(105,236)(106,235)
(107,234)(108,228)(109,232)(110,231)(111,230)(112,229)(113,248)(114,252)
(115,251)(116,250)(117,249)(118,243)(119,247)(120,246)(121,245)(122,244)
(123,238)(124,242)(125,241)(126,240)(127,239);;
s3 := (  3, 28)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 34)(  9, 33)( 10, 37)
( 11, 36)( 12, 35)( 13, 40)( 14, 39)( 15, 38)( 16, 42)( 17, 41)( 18, 46)
( 19, 45)( 20, 44)( 21, 43)( 22, 47)( 23, 52)( 24, 51)( 25, 50)( 26, 49)
( 27, 48)( 53,103)( 54,107)( 55,106)( 56,105)( 57,104)( 58,109)( 59,108)
( 60,112)( 61,111)( 62,110)( 63,115)( 64,114)( 65,113)( 66,117)( 67,116)
( 68,121)( 69,120)( 70,119)( 71,118)( 72,122)( 73,127)( 74,126)( 75,125)
( 76,124)( 77,123)( 79, 82)( 80, 81)( 83, 84)( 85, 87)( 88, 90)( 91, 92)
( 93, 96)( 94, 95)( 98,102)( 99,101)(128,153)(129,157)(130,156)(131,155)
(132,154)(133,159)(134,158)(135,162)(136,161)(137,160)(138,165)(139,164)
(140,163)(141,167)(142,166)(143,171)(144,170)(145,169)(146,168)(147,172)
(148,177)(149,176)(150,175)(151,174)(152,173)(178,228)(179,232)(180,231)
(181,230)(182,229)(183,234)(184,233)(185,237)(186,236)(187,235)(188,240)
(189,239)(190,238)(191,242)(192,241)(193,246)(194,245)(195,244)(196,243)
(197,247)(198,252)(199,251)(200,250)(201,249)(202,248)(204,207)(205,206)
(208,209)(210,212)(213,215)(216,217)(218,221)(219,220)(223,227)(224,226);;
s4 := (  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 28,103)( 29,107)( 30,106)( 31,105)( 32,104)( 33,108)
( 34,112)( 35,111)( 36,110)( 37,109)( 38,113)( 39,117)( 40,116)( 41,115)
( 42,114)( 43,118)( 44,122)( 45,121)( 46,120)( 47,119)( 48,123)( 49,127)
( 50,126)( 51,125)( 52,124)( 53, 78)( 54, 82)( 55, 81)( 56, 80)( 57, 79)
( 58, 83)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 88)( 64, 92)( 65, 91)
( 66, 90)( 67, 89)( 68, 93)( 69, 97)( 70, 96)( 71, 95)( 72, 94)( 73, 98)
( 74,102)( 75,101)( 76,100)( 77, 99)(129,132)(130,131)(134,137)(135,136)
(139,142)(140,141)(144,147)(145,146)(149,152)(150,151)(153,228)(154,232)
(155,231)(156,230)(157,229)(158,233)(159,237)(160,236)(161,235)(162,234)
(163,238)(164,242)(165,241)(166,240)(167,239)(168,243)(169,247)(170,246)
(171,245)(172,244)(173,248)(174,252)(175,251)(176,250)(177,249)(178,203)
(179,207)(180,206)(181,205)(182,204)(183,208)(184,212)(185,211)(186,210)
(187,209)(188,213)(189,217)(190,216)(191,215)(192,214)(193,218)(194,222)
(195,221)(196,220)(197,219)(198,223)(199,227)(200,226)(201,225)(202,224);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 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)( 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);
s2 := Sym(252)!(  3,133)(  4,137)(  5,136)(  6,135)(  7,134)(  8,128)(  9,132)
( 10,131)( 11,130)( 12,129)( 13,148)( 14,152)( 15,151)( 16,150)( 17,149)
( 18,143)( 19,147)( 20,146)( 21,145)( 22,144)( 23,138)( 24,142)( 25,141)
( 26,140)( 27,139)( 28,158)( 29,162)( 30,161)( 31,160)( 32,159)( 33,153)
( 34,157)( 35,156)( 36,155)( 37,154)( 38,173)( 39,177)( 40,176)( 41,175)
( 42,174)( 43,168)( 44,172)( 45,171)( 46,170)( 47,169)( 48,163)( 49,167)
( 50,166)( 51,165)( 52,164)( 53,183)( 54,187)( 55,186)( 56,185)( 57,184)
( 58,178)( 59,182)( 60,181)( 61,180)( 62,179)( 63,198)( 64,202)( 65,201)
( 66,200)( 67,199)( 68,193)( 69,197)( 70,196)( 71,195)( 72,194)( 73,188)
( 74,192)( 75,191)( 76,190)( 77,189)( 78,208)( 79,212)( 80,211)( 81,210)
( 82,209)( 83,203)( 84,207)( 85,206)( 86,205)( 87,204)( 88,223)( 89,227)
( 90,226)( 91,225)( 92,224)( 93,218)( 94,222)( 95,221)( 96,220)( 97,219)
( 98,213)( 99,217)(100,216)(101,215)(102,214)(103,233)(104,237)(105,236)
(106,235)(107,234)(108,228)(109,232)(110,231)(111,230)(112,229)(113,248)
(114,252)(115,251)(116,250)(117,249)(118,243)(119,247)(120,246)(121,245)
(122,244)(123,238)(124,242)(125,241)(126,240)(127,239);
s3 := Sym(252)!(  3, 28)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 34)(  9, 33)
( 10, 37)( 11, 36)( 12, 35)( 13, 40)( 14, 39)( 15, 38)( 16, 42)( 17, 41)
( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 47)( 23, 52)( 24, 51)( 25, 50)
( 26, 49)( 27, 48)( 53,103)( 54,107)( 55,106)( 56,105)( 57,104)( 58,109)
( 59,108)( 60,112)( 61,111)( 62,110)( 63,115)( 64,114)( 65,113)( 66,117)
( 67,116)( 68,121)( 69,120)( 70,119)( 71,118)( 72,122)( 73,127)( 74,126)
( 75,125)( 76,124)( 77,123)( 79, 82)( 80, 81)( 83, 84)( 85, 87)( 88, 90)
( 91, 92)( 93, 96)( 94, 95)( 98,102)( 99,101)(128,153)(129,157)(130,156)
(131,155)(132,154)(133,159)(134,158)(135,162)(136,161)(137,160)(138,165)
(139,164)(140,163)(141,167)(142,166)(143,171)(144,170)(145,169)(146,168)
(147,172)(148,177)(149,176)(150,175)(151,174)(152,173)(178,228)(179,232)
(180,231)(181,230)(182,229)(183,234)(184,233)(185,237)(186,236)(187,235)
(188,240)(189,239)(190,238)(191,242)(192,241)(193,246)(194,245)(195,244)
(196,243)(197,247)(198,252)(199,251)(200,250)(201,249)(202,248)(204,207)
(205,206)(208,209)(210,212)(213,215)(216,217)(218,221)(219,220)(223,227)
(224,226);
s4 := Sym(252)!(  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 28,103)( 29,107)( 30,106)( 31,105)( 32,104)
( 33,108)( 34,112)( 35,111)( 36,110)( 37,109)( 38,113)( 39,117)( 40,116)
( 41,115)( 42,114)( 43,118)( 44,122)( 45,121)( 46,120)( 47,119)( 48,123)
( 49,127)( 50,126)( 51,125)( 52,124)( 53, 78)( 54, 82)( 55, 81)( 56, 80)
( 57, 79)( 58, 83)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 88)( 64, 92)
( 65, 91)( 66, 90)( 67, 89)( 68, 93)( 69, 97)( 70, 96)( 71, 95)( 72, 94)
( 73, 98)( 74,102)( 75,101)( 76,100)( 77, 99)(129,132)(130,131)(134,137)
(135,136)(139,142)(140,141)(144,147)(145,146)(149,152)(150,151)(153,228)
(154,232)(155,231)(156,230)(157,229)(158,233)(159,237)(160,236)(161,235)
(162,234)(163,238)(164,242)(165,241)(166,240)(167,239)(168,243)(169,247)
(170,246)(171,245)(172,244)(173,248)(174,252)(175,251)(176,250)(177,249)
(178,203)(179,207)(180,206)(181,205)(182,204)(183,208)(184,212)(185,211)
(186,210)(187,209)(188,213)(189,217)(190,216)(191,215)(192,214)(193,218)
(194,222)(195,221)(196,220)(197,219)(198,223)(199,227)(200,226)(201,225)
(202,224);
poly := sub<Sym(252)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope