Polytope of Type {2,10,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,40}*1600a
if this polytope has a name.
Group : SmallGroup(1600,8115)
Rank : 4
Schlafli Type : {2,10,40}
Number of vertices, edges, etc : 2, 10, 200, 40
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 : {2,10,20}*800a
   4-fold quotients : {2,10,10}*400a
   5-fold quotients : {2,2,40}*320, {2,10,8}*320
   10-fold quotients : {2,2,20}*160, {2,10,4}*160
   20-fold quotients : {2,2,10}*80, {2,10,2}*80
   25-fold quotients : {2,2,8}*64
   40-fold quotients : {2,2,5}*40, {2,5,2}*40
   50-fold quotients : {2,2,4}*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)( 54, 57)( 55, 56)( 59, 62)( 60, 61)
( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)( 80, 81)
( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101)
(104,107)(105,106)(109,112)(110,111)(114,117)(115,116)(119,122)(120,121)
(124,127)(125,126)(129,132)(130,131)(134,137)(135,136)(139,142)(140,141)
(144,147)(145,146)(149,152)(150,151)(154,157)(155,156)(159,162)(160,161)
(164,167)(165,166)(169,172)(170,171)(174,177)(175,176)(179,182)(180,181)
(184,187)(185,186)(189,192)(190,191)(194,197)(195,196)(199,202)(200,201);;
s2 := (  3,  4)(  5,  7)(  8, 24)(  9, 23)( 10, 27)( 11, 26)( 12, 25)( 13, 19)
( 14, 18)( 15, 22)( 16, 21)( 17, 20)( 28, 29)( 30, 32)( 33, 49)( 34, 48)
( 35, 52)( 36, 51)( 37, 50)( 38, 44)( 39, 43)( 40, 47)( 41, 46)( 42, 45)
( 53, 79)( 54, 78)( 55, 82)( 56, 81)( 57, 80)( 58, 99)( 59, 98)( 60,102)
( 61,101)( 62,100)( 63, 94)( 64, 93)( 65, 97)( 66, 96)( 67, 95)( 68, 89)
( 69, 88)( 70, 92)( 71, 91)( 72, 90)( 73, 84)( 74, 83)( 75, 87)( 76, 86)
( 77, 85)(103,154)(104,153)(105,157)(106,156)(107,155)(108,174)(109,173)
(110,177)(111,176)(112,175)(113,169)(114,168)(115,172)(116,171)(117,170)
(118,164)(119,163)(120,167)(121,166)(122,165)(123,159)(124,158)(125,162)
(126,161)(127,160)(128,179)(129,178)(130,182)(131,181)(132,180)(133,199)
(134,198)(135,202)(136,201)(137,200)(138,194)(139,193)(140,197)(141,196)
(142,195)(143,189)(144,188)(145,192)(146,191)(147,190)(148,184)(149,183)
(150,187)(151,186)(152,185);;
s3 := (  3,108)(  4,109)(  5,110)(  6,111)(  7,112)(  8,103)(  9,104)( 10,105)
( 11,106)( 12,107)( 13,123)( 14,124)( 15,125)( 16,126)( 17,127)( 18,118)
( 19,119)( 20,120)( 21,121)( 22,122)( 23,113)( 24,114)( 25,115)( 26,116)
( 27,117)( 28,133)( 29,134)( 30,135)( 31,136)( 32,137)( 33,128)( 34,129)
( 35,130)( 36,131)( 37,132)( 38,148)( 39,149)( 40,150)( 41,151)( 42,152)
( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)( 48,138)( 49,139)( 50,140)
( 51,141)( 52,142)( 53,183)( 54,184)( 55,185)( 56,186)( 57,187)( 58,178)
( 59,179)( 60,180)( 61,181)( 62,182)( 63,198)( 64,199)( 65,200)( 66,201)
( 67,202)( 68,193)( 69,194)( 70,195)( 71,196)( 72,197)( 73,188)( 74,189)
( 75,190)( 76,191)( 77,192)( 78,158)( 79,159)( 80,160)( 81,161)( 82,162)
( 83,153)( 84,154)( 85,155)( 86,156)( 87,157)( 88,173)( 89,174)( 90,175)
( 91,176)( 92,177)( 93,168)( 94,169)( 95,170)( 96,171)( 97,172)( 98,163)
( 99,164)(100,165)(101,166)(102,167);;
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*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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)( 54, 57)( 55, 56)( 59, 62)
( 60, 61)( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)
( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)
(100,101)(104,107)(105,106)(109,112)(110,111)(114,117)(115,116)(119,122)
(120,121)(124,127)(125,126)(129,132)(130,131)(134,137)(135,136)(139,142)
(140,141)(144,147)(145,146)(149,152)(150,151)(154,157)(155,156)(159,162)
(160,161)(164,167)(165,166)(169,172)(170,171)(174,177)(175,176)(179,182)
(180,181)(184,187)(185,186)(189,192)(190,191)(194,197)(195,196)(199,202)
(200,201);
s2 := Sym(202)!(  3,  4)(  5,  7)(  8, 24)(  9, 23)( 10, 27)( 11, 26)( 12, 25)
( 13, 19)( 14, 18)( 15, 22)( 16, 21)( 17, 20)( 28, 29)( 30, 32)( 33, 49)
( 34, 48)( 35, 52)( 36, 51)( 37, 50)( 38, 44)( 39, 43)( 40, 47)( 41, 46)
( 42, 45)( 53, 79)( 54, 78)( 55, 82)( 56, 81)( 57, 80)( 58, 99)( 59, 98)
( 60,102)( 61,101)( 62,100)( 63, 94)( 64, 93)( 65, 97)( 66, 96)( 67, 95)
( 68, 89)( 69, 88)( 70, 92)( 71, 91)( 72, 90)( 73, 84)( 74, 83)( 75, 87)
( 76, 86)( 77, 85)(103,154)(104,153)(105,157)(106,156)(107,155)(108,174)
(109,173)(110,177)(111,176)(112,175)(113,169)(114,168)(115,172)(116,171)
(117,170)(118,164)(119,163)(120,167)(121,166)(122,165)(123,159)(124,158)
(125,162)(126,161)(127,160)(128,179)(129,178)(130,182)(131,181)(132,180)
(133,199)(134,198)(135,202)(136,201)(137,200)(138,194)(139,193)(140,197)
(141,196)(142,195)(143,189)(144,188)(145,192)(146,191)(147,190)(148,184)
(149,183)(150,187)(151,186)(152,185);
s3 := Sym(202)!(  3,108)(  4,109)(  5,110)(  6,111)(  7,112)(  8,103)(  9,104)
( 10,105)( 11,106)( 12,107)( 13,123)( 14,124)( 15,125)( 16,126)( 17,127)
( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,113)( 24,114)( 25,115)
( 26,116)( 27,117)( 28,133)( 29,134)( 30,135)( 31,136)( 32,137)( 33,128)
( 34,129)( 35,130)( 36,131)( 37,132)( 38,148)( 39,149)( 40,150)( 41,151)
( 42,152)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)( 48,138)( 49,139)
( 50,140)( 51,141)( 52,142)( 53,183)( 54,184)( 55,185)( 56,186)( 57,187)
( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,198)( 64,199)( 65,200)
( 66,201)( 67,202)( 68,193)( 69,194)( 70,195)( 71,196)( 72,197)( 73,188)
( 74,189)( 75,190)( 76,191)( 77,192)( 78,158)( 79,159)( 80,160)( 81,161)
( 82,162)( 83,153)( 84,154)( 85,155)( 86,156)( 87,157)( 88,173)( 89,174)
( 90,175)( 91,176)( 92,177)( 93,168)( 94,169)( 95,170)( 96,171)( 97,172)
( 98,163)( 99,164)(100,165)(101,166)(102,167);
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*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope