Polytope of Type {2,40,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,40,10}*1600c
if this polytope has a name.
Group : SmallGroup(1600,8648)
Rank : 4
Schlafli Type : {2,40,10}
Number of vertices, edges, etc : 2, 40, 200, 10
Order of s₀s₁s₂s₃ : 40
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 : {2,20,10}*800c
   4-fold quotients : {2,10,10}*400b
   5-fold quotients : {2,8,10}*320
   8-fold quotients : {2,10,5}*200
   10-fold quotients : {2,4,10}*160
   20-fold quotients : {2,2,10}*80
   25-fold quotients : {2,8,2}*64
   40-fold quotients : {2,2,5}*40
   50-fold quotients : {2,4,2}*32
   100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.

Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 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)(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)(128,178)(129,182)(130,181)(131,180)(132,179)(133,183)(134,187)(135,186)(136,185)(137,184)(138,188)(139,192)(140,191)(141,190)(142,189)(143,193)(144,197)(145,196)(146,195)(147,194)(148,198)(149,202)(150,201)(151,200)(152,199);;
s2 := (  3,104)(  4,103)(  5,107)(  6,106)(  7,105)(  8,124)(  9,123)( 10,127)( 11,126)( 12,125)( 13,119)( 14,118)( 15,122)( 16,121)( 17,120)( 18,114)( 19,113)( 20,117)( 21,116)( 22,115)( 23,109)( 24,108)( 25,112)( 26,111)( 27,110)( 28,129)( 29,128)( 30,132)( 31,131)( 32,130)( 33,149)( 34,148)( 35,152)( 36,151)( 37,150)( 38,144)( 39,143)( 40,147)( 41,146)( 42,145)( 43,139)( 44,138)( 45,142)( 46,141)( 47,140)( 48,134)( 49,133)( 50,137)( 51,136)( 52,135)( 53,179)( 54,178)( 55,182)( 56,181)( 57,180)( 58,199)( 59,198)( 60,202)( 61,201)( 62,200)( 63,194)( 64,193)( 65,197)( 66,196)( 67,195)( 68,189)( 69,188)( 70,192)( 71,191)( 72,190)( 73,184)( 74,183)( 75,187)( 76,186)( 77,185)( 78,154)( 79,153)( 80,157)( 81,156)( 82,155)( 83,174)( 84,173)( 85,177)( 86,176)( 87,175)( 88,169)( 89,168)( 90,172)( 91,171)( 92,170)( 93,164)( 94,163)( 95,167)( 96,166)( 97,165)( 98,159)( 99,158)(100,162)(101,161)(102,160);;
s3 := (  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);;
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*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope