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

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

to this polytope