Polytope of Type {20,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,20}*800a
Also Known As : {20,20|2}. if this polytope has another name.
Group : SmallGroup(800,700)
Rank : 3
Schlafli Type : {20,20}
Number of vertices, edges, etc : 20, 200, 20
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {20,20,2} of size 1600
Vertex Figure Of :
   {2,20,20} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,20}*400a, {20,10}*400a
   4-fold quotients : {10,10}*200a
   5-fold quotients : {4,20}*160, {20,4}*160
   10-fold quotients : {2,20}*80, {20,2}*80, {4,10}*80, {10,4}*80
   20-fold quotients : {2,10}*40, {10,2}*40
   25-fold quotients : {4,4}*32
   40-fold quotients : {2,5}*20, {5,2}*20
   50-fold quotients : {2,4}*16, {4,2}*16
   100-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,20}*1600a, {20,40}*1600c, {40,20}*1600c, {20,40}*1600e, {40,20}*1600e
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope