Polytope of Type {2,50,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,50,8}*1600
if this polytope has a name.
Group : SmallGroup(1600,1429)
Rank : 4
Schlafli Type : {2,50,8}
Number of vertices, edges, etc : 2, 50, 200, 8
Order of s₀s₁s₂s₃ : 200
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 : {2,50,4}*800
   4-fold quotients : {2,50,2}*400
   5-fold quotients : {2,10,8}*320
   8-fold quotients : {2,25,2}*200
   10-fold quotients : {2,10,4}*160
   20-fold quotients : {2,10,2}*80
   25-fold quotients : {2,2,8}*64
   40-fold quotients : {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)(  8, 27)(  9, 26)( 10, 25)( 11, 24)( 12, 23)( 13, 22)
( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 29, 32)( 30, 31)( 33, 52)( 34, 51)
( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)( 42, 43)
( 54, 57)( 55, 56)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)
( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 79, 82)( 80, 81)( 83,102)( 84,101)
( 85,100)( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 92, 93)
(104,107)(105,106)(108,127)(109,126)(110,125)(111,124)(112,123)(113,122)
(114,121)(115,120)(116,119)(117,118)(129,132)(130,131)(133,152)(134,151)
(135,150)(136,149)(137,148)(138,147)(139,146)(140,145)(141,144)(142,143)
(154,157)(155,156)(158,177)(159,176)(160,175)(161,174)(162,173)(163,172)
(164,171)(165,170)(166,169)(167,168)(179,182)(180,181)(183,202)(184,201)
(185,200)(186,199)(187,198)(188,197)(189,196)(190,195)(191,194)(192,193);;
s2 := (  3,  8)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 13, 27)( 14, 26)( 15, 25)
( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 28, 33)( 29, 37)( 30, 36)( 31, 35)
( 32, 34)( 38, 52)( 39, 51)( 40, 50)( 41, 49)( 42, 48)( 43, 47)( 44, 46)
( 53, 83)( 54, 87)( 55, 86)( 56, 85)( 57, 84)( 58, 78)( 59, 82)( 60, 81)
( 61, 80)( 62, 79)( 63,102)( 64,101)( 65,100)( 66, 99)( 67, 98)( 68, 97)
( 69, 96)( 70, 95)( 71, 94)( 72, 93)( 73, 92)( 74, 91)( 75, 90)( 76, 89)
( 77, 88)(103,158)(104,162)(105,161)(106,160)(107,159)(108,153)(109,157)
(110,156)(111,155)(112,154)(113,177)(114,176)(115,175)(116,174)(117,173)
(118,172)(119,171)(120,170)(121,169)(122,168)(123,167)(124,166)(125,165)
(126,164)(127,163)(128,183)(129,187)(130,186)(131,185)(132,184)(133,178)
(134,182)(135,181)(136,180)(137,179)(138,202)(139,201)(140,200)(141,199)
(142,198)(143,197)(144,196)(145,195)(146,194)(147,193)(148,192)(149,191)
(150,190)(151,189)(152,188);;
s3 := (  3,103)(  4,104)(  5,105)(  6,106)(  7,107)(  8,108)(  9,109)( 10,110)
( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)( 17,117)( 18,118)
( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)( 25,125)( 26,126)
( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)( 32,132)( 33,133)( 34,134)
( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)( 40,140)( 41,141)( 42,142)
( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)( 48,148)( 49,149)( 50,150)
( 51,151)( 52,152)( 53,178)( 54,179)( 55,180)( 56,181)( 57,182)( 58,183)
( 59,184)( 60,185)( 61,186)( 62,187)( 63,188)( 64,189)( 65,190)( 66,191)
( 67,192)( 68,193)( 69,194)( 70,195)( 71,196)( 72,197)( 73,198)( 74,199)
( 75,200)( 76,201)( 77,202)( 78,153)( 79,154)( 80,155)( 81,156)( 82,157)
( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)( 89,164)( 90,165)
( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)( 97,172)( 98,173)
( 99,174)(100,175)(101,176)(102,177);;
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, 
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*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, 27)(  9, 26)( 10, 25)( 11, 24)( 12, 23)
( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 29, 32)( 30, 31)( 33, 52)
( 34, 51)( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)
( 42, 43)( 54, 57)( 55, 56)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 79, 82)( 80, 81)( 83,102)
( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)
( 92, 93)(104,107)(105,106)(108,127)(109,126)(110,125)(111,124)(112,123)
(113,122)(114,121)(115,120)(116,119)(117,118)(129,132)(130,131)(133,152)
(134,151)(135,150)(136,149)(137,148)(138,147)(139,146)(140,145)(141,144)
(142,143)(154,157)(155,156)(158,177)(159,176)(160,175)(161,174)(162,173)
(163,172)(164,171)(165,170)(166,169)(167,168)(179,182)(180,181)(183,202)
(184,201)(185,200)(186,199)(187,198)(188,197)(189,196)(190,195)(191,194)
(192,193);
s2 := Sym(202)!(  3,  8)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 13, 27)( 14, 26)
( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 28, 33)( 29, 37)( 30, 36)
( 31, 35)( 32, 34)( 38, 52)( 39, 51)( 40, 50)( 41, 49)( 42, 48)( 43, 47)
( 44, 46)( 53, 83)( 54, 87)( 55, 86)( 56, 85)( 57, 84)( 58, 78)( 59, 82)
( 60, 81)( 61, 80)( 62, 79)( 63,102)( 64,101)( 65,100)( 66, 99)( 67, 98)
( 68, 97)( 69, 96)( 70, 95)( 71, 94)( 72, 93)( 73, 92)( 74, 91)( 75, 90)
( 76, 89)( 77, 88)(103,158)(104,162)(105,161)(106,160)(107,159)(108,153)
(109,157)(110,156)(111,155)(112,154)(113,177)(114,176)(115,175)(116,174)
(117,173)(118,172)(119,171)(120,170)(121,169)(122,168)(123,167)(124,166)
(125,165)(126,164)(127,163)(128,183)(129,187)(130,186)(131,185)(132,184)
(133,178)(134,182)(135,181)(136,180)(137,179)(138,202)(139,201)(140,200)
(141,199)(142,198)(143,197)(144,196)(145,195)(146,194)(147,193)(148,192)
(149,191)(150,190)(151,189)(152,188);
s3 := Sym(202)!(  3,103)(  4,104)(  5,105)(  6,106)(  7,107)(  8,108)(  9,109)
( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)( 17,117)
( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)( 25,125)
( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)( 32,132)( 33,133)
( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)( 40,140)( 41,141)
( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)( 48,148)( 49,149)
( 50,150)( 51,151)( 52,152)( 53,178)( 54,179)( 55,180)( 56,181)( 57,182)
( 58,183)( 59,184)( 60,185)( 61,186)( 62,187)( 63,188)( 64,189)( 65,190)
( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,196)( 72,197)( 73,198)
( 74,199)( 75,200)( 76,201)( 77,202)( 78,153)( 79,154)( 80,155)( 81,156)
( 82,157)( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)( 89,164)
( 90,165)( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)( 97,172)
( 98,173)( 99,174)(100,175)(101,176)(102,177);
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, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope