Polytope of Type {2,20,20}

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

Permutation Representation (Magma) :

s0 := Sym(202)!(1,2);
s1 := 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);
s2 := Sym(202)!(  3,104)(  4,103)(  5,107)(  6,106)(  7,105)(  8,124)(  9,123)
( 10,127)( 11,126)( 12,125)( 13,119)( 14,118)( 15,122)( 16,121)( 17,120)
( 18,114)( 19,113)( 20,117)( 21,116)( 22,115)( 23,109)( 24,108)( 25,112)
( 26,111)( 27,110)( 28,129)( 29,128)( 30,132)( 31,131)( 32,130)( 33,149)
( 34,148)( 35,152)( 36,151)( 37,150)( 38,144)( 39,143)( 40,147)( 41,146)
( 42,145)( 43,139)( 44,138)( 45,142)( 46,141)( 47,140)( 48,134)( 49,133)
( 50,137)( 51,136)( 52,135)( 53,154)( 54,153)( 55,157)( 56,156)( 57,155)
( 58,174)( 59,173)( 60,177)( 61,176)( 62,175)( 63,169)( 64,168)( 65,172)
( 66,171)( 67,170)( 68,164)( 69,163)( 70,167)( 71,166)( 72,165)( 73,159)
( 74,158)( 75,162)( 76,161)( 77,160)( 78,179)( 79,178)( 80,182)( 81,181)
( 82,180)( 83,199)( 84,198)( 85,202)( 86,201)( 87,200)( 88,194)( 89,193)
( 90,197)( 91,196)( 92,195)( 93,189)( 94,188)( 95,192)( 96,191)( 97,190)
( 98,184)( 99,183)(100,187)(101,186)(102,185);
s3 := Sym(202)!(  3,  8)(  4,  9)(  5, 10)(  6, 11)(  7, 12)( 13, 23)( 14, 24)
( 15, 25)( 16, 26)( 17, 27)( 28, 33)( 29, 34)( 30, 35)( 31, 36)( 32, 37)
( 38, 48)( 39, 49)( 40, 50)( 41, 51)( 42, 52)( 53, 58)( 54, 59)( 55, 60)
( 56, 61)( 57, 62)( 63, 73)( 64, 74)( 65, 75)( 66, 76)( 67, 77)( 78, 83)
( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 88, 98)( 89, 99)( 90,100)( 91,101)
( 92,102)(103,158)(104,159)(105,160)(106,161)(107,162)(108,153)(109,154)
(110,155)(111,156)(112,157)(113,173)(114,174)(115,175)(116,176)(117,177)
(118,168)(119,169)(120,170)(121,171)(122,172)(123,163)(124,164)(125,165)
(126,166)(127,167)(128,183)(129,184)(130,185)(131,186)(132,187)(133,178)
(134,179)(135,180)(136,181)(137,182)(138,198)(139,199)(140,200)(141,201)
(142,202)(143,193)(144,194)(145,195)(146,196)(147,197)(148,188)(149,189)
(150,190)(151,191)(152,192);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope