Polytope of Type {2,40,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,40,10}*1600b
if this polytope has a name.
Group : SmallGroup(1600,8115)
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}*800b
   4-fold quotients : {2,10,10}*400c
   5-fold quotients : {2,40,2}*320
   8-fold quotients : {2,5,10}*200
   10-fold quotients : {2,20,2}*160
   20-fold quotients : {2,10,2}*80
   25-fold quotients : {2,8,2}*64
   40-fold quotients : {2,5,2}*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)(  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)
( 53, 78)( 54, 82)( 55, 81)( 56, 80)( 57, 79)( 58, 98)( 59,102)( 60,101)
( 61,100)( 62, 99)( 63, 93)( 64, 97)( 65, 96)( 66, 95)( 67, 94)( 68, 88)
( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 83)( 74, 87)( 75, 86)( 76, 85)
( 77, 84)(103,153)(104,157)(105,156)(106,155)(107,154)(108,173)(109,177)
(110,176)(111,175)(112,174)(113,168)(114,172)(115,171)(116,170)(117,169)
(118,163)(119,167)(120,166)(121,165)(122,164)(123,158)(124,162)(125,161)
(126,160)(127,159)(128,178)(129,182)(130,181)(131,180)(132,179)(133,198)
(134,202)(135,201)(136,200)(137,199)(138,193)(139,197)(140,196)(141,195)
(142,194)(143,188)(144,192)(145,191)(146,190)(147,189)(148,183)(149,187)
(150,186)(151,185)(152,184);;
s2 := (  3,109)(  4,108)(  5,112)(  6,111)(  7,110)(  8,104)(  9,103)( 10,107)
( 11,106)( 12,105)( 13,124)( 14,123)( 15,127)( 16,126)( 17,125)( 18,119)
( 19,118)( 20,122)( 21,121)( 22,120)( 23,114)( 24,113)( 25,117)( 26,116)
( 27,115)( 28,134)( 29,133)( 30,137)( 31,136)( 32,135)( 33,129)( 34,128)
( 35,132)( 36,131)( 37,130)( 38,149)( 39,148)( 40,152)( 41,151)( 42,150)
( 43,144)( 44,143)( 45,147)( 46,146)( 47,145)( 48,139)( 49,138)( 50,142)
( 51,141)( 52,140)( 53,184)( 54,183)( 55,187)( 56,186)( 57,185)( 58,179)
( 59,178)( 60,182)( 61,181)( 62,180)( 63,199)( 64,198)( 65,202)( 66,201)
( 67,200)( 68,194)( 69,193)( 70,197)( 71,196)( 72,195)( 73,189)( 74,188)
( 75,192)( 76,191)( 77,190)( 78,159)( 79,158)( 80,162)( 81,161)( 82,160)
( 83,154)( 84,153)( 85,157)( 86,156)( 87,155)( 88,174)( 89,173)( 90,177)
( 91,176)( 92,175)( 93,169)( 94,168)( 95,172)( 96,171)( 97,170)( 98,164)
( 99,163)(100,167)(101,166)(102,165);;
s3 := (  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);;
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, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(202)!(1,2);
s1 := Sym(202)!(  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)( 53, 78)( 54, 82)( 55, 81)( 56, 80)( 57, 79)( 58, 98)( 59,102)
( 60,101)( 61,100)( 62, 99)( 63, 93)( 64, 97)( 65, 96)( 66, 95)( 67, 94)
( 68, 88)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 83)( 74, 87)( 75, 86)
( 76, 85)( 77, 84)(103,153)(104,157)(105,156)(106,155)(107,154)(108,173)
(109,177)(110,176)(111,175)(112,174)(113,168)(114,172)(115,171)(116,170)
(117,169)(118,163)(119,167)(120,166)(121,165)(122,164)(123,158)(124,162)
(125,161)(126,160)(127,159)(128,178)(129,182)(130,181)(131,180)(132,179)
(133,198)(134,202)(135,201)(136,200)(137,199)(138,193)(139,197)(140,196)
(141,195)(142,194)(143,188)(144,192)(145,191)(146,190)(147,189)(148,183)
(149,187)(150,186)(151,185)(152,184);
s2 := Sym(202)!(  3,109)(  4,108)(  5,112)(  6,111)(  7,110)(  8,104)(  9,103)
( 10,107)( 11,106)( 12,105)( 13,124)( 14,123)( 15,127)( 16,126)( 17,125)
( 18,119)( 19,118)( 20,122)( 21,121)( 22,120)( 23,114)( 24,113)( 25,117)
( 26,116)( 27,115)( 28,134)( 29,133)( 30,137)( 31,136)( 32,135)( 33,129)
( 34,128)( 35,132)( 36,131)( 37,130)( 38,149)( 39,148)( 40,152)( 41,151)
( 42,150)( 43,144)( 44,143)( 45,147)( 46,146)( 47,145)( 48,139)( 49,138)
( 50,142)( 51,141)( 52,140)( 53,184)( 54,183)( 55,187)( 56,186)( 57,185)
( 58,179)( 59,178)( 60,182)( 61,181)( 62,180)( 63,199)( 64,198)( 65,202)
( 66,201)( 67,200)( 68,194)( 69,193)( 70,197)( 71,196)( 72,195)( 73,189)
( 74,188)( 75,192)( 76,191)( 77,190)( 78,159)( 79,158)( 80,162)( 81,161)
( 82,160)( 83,154)( 84,153)( 85,157)( 86,156)( 87,155)( 88,174)( 89,173)
( 90,177)( 91,176)( 92,175)( 93,169)( 94,168)( 95,172)( 96,171)( 97,170)
( 98,164)( 99,163)(100,167)(101,166)(102,165);
s3 := 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);
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope