Polytope of Type {2,40,10}

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