Polytope of Type {2,20,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,20}*1600c
if this polytope has a name.
Group : SmallGroup(1600,8514)
Rank : 4
Schlafli Type : {2,20,20}
Number of vertices, edges, etc : 2, 20, 200, 20
Order of s₀s₁s₂s₃ : 20
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, {2,10,20}*800c
   4-fold quotients : {2,10,10}*400c
   5-fold quotients : {2,20,4}*320
   8-fold quotients : {2,5,10}*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, 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)
( 54, 57)( 55, 56)( 58, 73)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 68)
( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 79, 82)( 80, 81)( 83, 98)( 84,102)
( 85,101)( 86,100)( 87, 99)( 88, 93)( 89, 97)( 90, 96)( 91, 95)( 92, 94)
(103,178)(104,182)(105,181)(106,180)(107,179)(108,198)(109,202)(110,201)
(111,200)(112,199)(113,193)(114,197)(115,196)(116,195)(117,194)(118,188)
(119,192)(120,191)(121,190)(122,189)(123,183)(124,187)(125,186)(126,185)
(127,184)(128,153)(129,157)(130,156)(131,155)(132,154)(133,173)(134,177)
(135,176)(136,175)(137,174)(138,168)(139,172)(140,171)(141,170)(142,169)
(143,163)(144,167)(145,166)(146,165)(147,164)(148,158)(149,162)(150,161)
(151,160)(152,159);;
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)( 53,159)( 54,158)( 55,162)( 56,161)( 57,160)( 58,154)
( 59,153)( 60,157)( 61,156)( 62,155)( 63,174)( 64,173)( 65,177)( 66,176)
( 67,175)( 68,169)( 69,168)( 70,172)( 71,171)( 72,170)( 73,164)( 74,163)
( 75,167)( 76,166)( 77,165)( 78,184)( 79,183)( 80,187)( 81,186)( 82,185)
( 83,179)( 84,178)( 85,182)( 86,181)( 87,180)( 88,199)( 89,198)( 90,202)
( 91,201)( 92,200)( 93,194)( 94,193)( 95,197)( 96,196)( 97,195)( 98,189)
( 99,188)(100,192)(101,191)(102,190);;
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)
(103,128)(104,132)(105,131)(106,130)(107,129)(108,133)(109,137)(110,136)
(111,135)(112,134)(113,138)(114,142)(115,141)(116,140)(117,139)(118,143)
(119,147)(120,146)(121,145)(122,144)(123,148)(124,152)(125,151)(126,150)
(127,149)(153,178)(154,182)(155,181)(156,180)(157,179)(158,183)(159,187)
(160,186)(161,185)(162,184)(163,188)(164,192)(165,191)(166,190)(167,189)
(168,193)(169,197)(170,196)(171,195)(172,194)(173,198)(174,202)(175,201)
(176,200)(177,199);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s3*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)( 54, 57)( 55, 56)( 58, 73)( 59, 77)( 60, 76)( 61, 75)( 62, 74)
( 63, 68)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 79, 82)( 80, 81)( 83, 98)
( 84,102)( 85,101)( 86,100)( 87, 99)( 88, 93)( 89, 97)( 90, 96)( 91, 95)
( 92, 94)(103,178)(104,182)(105,181)(106,180)(107,179)(108,198)(109,202)
(110,201)(111,200)(112,199)(113,193)(114,197)(115,196)(116,195)(117,194)
(118,188)(119,192)(120,191)(121,190)(122,189)(123,183)(124,187)(125,186)
(126,185)(127,184)(128,153)(129,157)(130,156)(131,155)(132,154)(133,173)
(134,177)(135,176)(136,175)(137,174)(138,168)(139,172)(140,171)(141,170)
(142,169)(143,163)(144,167)(145,166)(146,165)(147,164)(148,158)(149,162)
(150,161)(151,160)(152,159);
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)( 53,159)( 54,158)( 55,162)( 56,161)( 57,160)
( 58,154)( 59,153)( 60,157)( 61,156)( 62,155)( 63,174)( 64,173)( 65,177)
( 66,176)( 67,175)( 68,169)( 69,168)( 70,172)( 71,171)( 72,170)( 73,164)
( 74,163)( 75,167)( 76,166)( 77,165)( 78,184)( 79,183)( 80,187)( 81,186)
( 82,185)( 83,179)( 84,178)( 85,182)( 86,181)( 87,180)( 88,199)( 89,198)
( 90,202)( 91,201)( 92,200)( 93,194)( 94,193)( 95,197)( 96,196)( 97,195)
( 98,189)( 99,188)(100,192)(101,191)(102,190);
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)(103,128)(104,132)(105,131)(106,130)(107,129)(108,133)(109,137)
(110,136)(111,135)(112,134)(113,138)(114,142)(115,141)(116,140)(117,139)
(118,143)(119,147)(120,146)(121,145)(122,144)(123,148)(124,152)(125,151)
(126,150)(127,149)(153,178)(154,182)(155,181)(156,180)(157,179)(158,183)
(159,187)(160,186)(161,185)(162,184)(163,188)(164,192)(165,191)(166,190)
(167,189)(168,193)(169,197)(170,196)(171,195)(172,194)(173,198)(174,202)
(175,201)(176,200)(177,199);
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope