Polytope of Type {2,100,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,100,4}*1600
if this polytope has a name.
Group : SmallGroup(1600,1163)
Rank : 4
Schlafli Type : {2,100,4}
Number of vertices, edges, etc : 2, 100, 200, 4
Order of s₀s₁s₂s₃ : 100
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 : {2,100,2}*800, {2,50,4}*800
   4-fold quotients : {2,50,2}*400
   5-fold quotients : {2,20,4}*320
   8-fold quotients : {2,25,2}*200
   10-fold quotients : {2,20,2}*160, {2,10,4}*160
   20-fold quotients : {2,10,2}*80
   25-fold quotients : {2,4,4}*64
   40-fold quotients : {2,5,2}*40
   50-fold quotients : {2,2,4}*32, {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, 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)
(103,153)(104,157)(105,156)(106,155)(107,154)(108,177)(109,176)(110,175)
(111,174)(112,173)(113,172)(114,171)(115,170)(116,169)(117,168)(118,167)
(119,166)(120,165)(121,164)(122,163)(123,162)(124,161)(125,160)(126,159)
(127,158)(128,178)(129,182)(130,181)(131,180)(132,179)(133,202)(134,201)
(135,200)(136,199)(137,198)(138,197)(139,196)(140,195)(141,194)(142,193)
(143,192)(144,191)(145,190)(146,189)(147,188)(148,187)(149,186)(150,185)
(151,184)(152,183);;
s2 := (  3,108)(  4,112)(  5,111)(  6,110)(  7,109)(  8,103)(  9,107)( 10,106)
( 11,105)( 12,104)( 13,127)( 14,126)( 15,125)( 16,124)( 17,123)( 18,122)
( 19,121)( 20,120)( 21,119)( 22,118)( 23,117)( 24,116)( 25,115)( 26,114)
( 27,113)( 28,133)( 29,137)( 30,136)( 31,135)( 32,134)( 33,128)( 34,132)
( 35,131)( 36,130)( 37,129)( 38,152)( 39,151)( 40,150)( 41,149)( 42,148)
( 43,147)( 44,146)( 45,145)( 46,144)( 47,143)( 48,142)( 49,141)( 50,140)
( 51,139)( 52,138)( 53,158)( 54,162)( 55,161)( 56,160)( 57,159)( 58,153)
( 59,157)( 60,156)( 61,155)( 62,154)( 63,177)( 64,176)( 65,175)( 66,174)
( 67,173)( 68,172)( 69,171)( 70,170)( 71,169)( 72,168)( 73,167)( 74,166)
( 75,165)( 76,164)( 77,163)( 78,183)( 79,187)( 80,186)( 81,185)( 82,184)
( 83,178)( 84,182)( 85,181)( 86,180)( 87,179)( 88,202)( 89,201)( 90,200)
( 91,199)( 92,198)( 93,197)( 94,196)( 95,195)( 96,194)( 97,193)( 98,192)
( 99,191)(100,190)(101,189)(102,188);;
s3 := (103,128)(104,129)(105,130)(106,131)(107,132)(108,133)(109,134)(110,135)
(111,136)(112,137)(113,138)(114,139)(115,140)(116,141)(117,142)(118,143)
(119,144)(120,145)(121,146)(122,147)(123,148)(124,149)(125,150)(126,151)
(127,152)(153,178)(154,179)(155,180)(156,181)(157,182)(158,183)(159,184)
(160,185)(161,186)(162,187)(163,188)(164,189)(165,190)(166,191)(167,192)
(168,193)(169,194)(170,195)(171,196)(172,197)(173,198)(174,199)(175,200)
(176,201)(177,202);;
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, 
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*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)(103,153)(104,157)(105,156)(106,155)(107,154)(108,177)(109,176)
(110,175)(111,174)(112,173)(113,172)(114,171)(115,170)(116,169)(117,168)
(118,167)(119,166)(120,165)(121,164)(122,163)(123,162)(124,161)(125,160)
(126,159)(127,158)(128,178)(129,182)(130,181)(131,180)(132,179)(133,202)
(134,201)(135,200)(136,199)(137,198)(138,197)(139,196)(140,195)(141,194)
(142,193)(143,192)(144,191)(145,190)(146,189)(147,188)(148,187)(149,186)
(150,185)(151,184)(152,183);
s2 := Sym(202)!(  3,108)(  4,112)(  5,111)(  6,110)(  7,109)(  8,103)(  9,107)
( 10,106)( 11,105)( 12,104)( 13,127)( 14,126)( 15,125)( 16,124)( 17,123)
( 18,122)( 19,121)( 20,120)( 21,119)( 22,118)( 23,117)( 24,116)( 25,115)
( 26,114)( 27,113)( 28,133)( 29,137)( 30,136)( 31,135)( 32,134)( 33,128)
( 34,132)( 35,131)( 36,130)( 37,129)( 38,152)( 39,151)( 40,150)( 41,149)
( 42,148)( 43,147)( 44,146)( 45,145)( 46,144)( 47,143)( 48,142)( 49,141)
( 50,140)( 51,139)( 52,138)( 53,158)( 54,162)( 55,161)( 56,160)( 57,159)
( 58,153)( 59,157)( 60,156)( 61,155)( 62,154)( 63,177)( 64,176)( 65,175)
( 66,174)( 67,173)( 68,172)( 69,171)( 70,170)( 71,169)( 72,168)( 73,167)
( 74,166)( 75,165)( 76,164)( 77,163)( 78,183)( 79,187)( 80,186)( 81,185)
( 82,184)( 83,178)( 84,182)( 85,181)( 86,180)( 87,179)( 88,202)( 89,201)
( 90,200)( 91,199)( 92,198)( 93,197)( 94,196)( 95,195)( 96,194)( 97,193)
( 98,192)( 99,191)(100,190)(101,189)(102,188);
s3 := Sym(202)!(103,128)(104,129)(105,130)(106,131)(107,132)(108,133)(109,134)
(110,135)(111,136)(112,137)(113,138)(114,139)(115,140)(116,141)(117,142)
(118,143)(119,144)(120,145)(121,146)(122,147)(123,148)(124,149)(125,150)
(126,151)(127,152)(153,178)(154,179)(155,180)(156,181)(157,182)(158,183)
(159,184)(160,185)(161,186)(162,187)(163,188)(164,189)(165,190)(166,191)
(167,192)(168,193)(169,194)(170,195)(171,196)(172,197)(173,198)(174,199)
(175,200)(176,201)(177,202);
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, 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*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