Polytope of Type {20,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,20}*800c
if this polytope has a 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 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {20,10}*400b, {10,20}*400c
   4-fold quotients : {10,10}*200c
   5-fold quotients : {20,4}*160
   8-fold quotients : {5,10}*100
   10-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {10,2}*40
   25-fold quotients : {4,4}*32
   40-fold quotients : {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 : {20,40}*1600a, {20,20}*1600c, {20,40}*1600b, {40,20}*1600d, {40,20}*1600f
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope