Polytope of Type {20,20} with group SmallGroup(800,700)

Overview

Group: SmallGroup(800,700)
Rank: 3
Schläfli Type: {20,20}
Vertices, edges, …: 20, 200, 20
Order of s₀s₁s₂: 20
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie

Quotients maximal quotients in bold

2-fold

4-fold

{10,10}*200b

5-fold

{4,20}*160

8-fold

{10,5}*100

10-fold

20-fold

{2,10}*40

25-fold

{4,4}*32

40-fold

{2,5}*20

50-fold

100-fold

{2,2}*8

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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