Polytope of Type {20,4} with group SmallGroup(2000,482)

Overview

Group: SmallGroup(2000,482)
Rank: 3
Schläfli Type: {20,4}
Vertices, edges, …: 250, 500, 50
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{20,4}*1000

5-fold

{4,4}*400

10-fold

{4,4}*200

250-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*(s2*s1*s0*s1)^3*s2> of order 2

25 facets

25 of {20}*40

125 vertex figures

125 of {4}*8

P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*(s1*s0)^3*s2*s1*s2> of order 2

26 facets

2 of {10}*20
24 of {20}*40

130 vertex figures

120 of {4}*8
10 of {2}*4

P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*(s1*s0)^3*s2*s1*s2, (s1*s2*s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 4

13 facets

1 of {10}*20
12 of {20}*40

65 vertex figures

60 of {4}*8
5 of {2}*4

P/N, where N=<(s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1> of order 5

10 facets

10 of {20}*40

50 vertex figures

50 of {4}*8

P/N, where N=<s0*s1*s2*s1*s0*s1*s2*(s1*s0)^2*s2*s1*s2> of order 5

10 facets

10 of {20}*40

50 vertex figures

50 of {4}*8

P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^2*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 10

6 facets

2 of {10}*20
4 of {20}*40

30 vertex figures

20 of {4}*8
10 of {2}*4

P/N, where N=<s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2, (s1*s2*s1*s0)^2*(s1*s2)^2> of order 10

6 facets

2 of {10}*20
4 of {20}*40

30 vertex figures

20 of {4}*8
10 of {2}*4

Representations

Permutation Representation (GAP)

s0 := (  2,  5)(  3,  4)(  6, 59)(  7, 58)(  8, 57)(  9, 56)( 10, 60)( 11,114)( 12,113)( 13,112)( 14,111)( 15,115)( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21,100)( 22, 99)( 23, 98)( 24, 97)( 25, 96)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31, 34)( 32, 33)( 36, 89)( 37, 88)( 38, 87)( 39, 86)( 40, 90)( 46, 75)( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 61, 64)( 62, 63)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 81,109)( 82,108)( 83,107)( 84,106)( 85,110)( 92, 95)( 93, 94)(121,125)(122,124)(127,130)(128,129)(131,184)(132,183)(133,182)(134,181)(135,185)(136,239)(137,238)(138,237)(139,236)(140,240)(141,166)(142,170)(143,169)(144,168)(145,167)(146,225)(147,224)(148,223)(149,222)(150,221)(151,226)(152,230)(153,229)(154,228)(155,227)(156,159)(157,158)(161,214)(162,213)(163,212)(164,211)(165,215)(171,200)(172,199)(173,198)(174,197)(175,196)(176,201)(177,205)(178,204)(179,203)(180,202)(186,189)(187,188)(191,241)(192,245)(193,244)(194,243)(195,242)(206,234)(207,233)(208,232)(209,231)(210,235)(217,220)(218,219)(246,250)(247,249);;
s1 := (  1,  3)(  4,  5)(  6, 43)(  7, 42)(  8, 41)(  9, 45)( 10, 44)( 11, 56)( 12, 60)( 13, 59)( 14, 58)( 15, 57)( 16, 97)( 17, 96)( 18,100)( 19, 99)( 20, 98)( 21,111)( 22,115)( 23,114)( 24,113)( 25,112)( 26, 63)( 27, 62)( 28, 61)( 29, 65)( 30, 64)( 31, 80)( 32, 79)( 33, 78)( 34, 77)( 35, 76)( 36,120)( 37,119)( 38,118)( 39,117)( 40,116)( 46, 49)( 47, 48)( 51,122)( 52,121)( 53,125)( 54,124)( 55,123)( 66, 68)( 69, 70)( 71, 81)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 86, 90)( 87, 89)( 91,102)( 92,101)( 93,105)( 94,104)( 95,103)(106,110)(107,109)(126,128)(129,130)(131,168)(132,167)(133,166)(134,170)(135,169)(136,181)(137,185)(138,184)(139,183)(140,182)(141,222)(142,221)(143,225)(144,224)(145,223)(146,236)(147,240)(148,239)(149,238)(150,237)(151,188)(152,187)(153,186)(154,190)(155,189)(156,205)(157,204)(158,203)(159,202)(160,201)(161,245)(162,244)(163,243)(164,242)(165,241)(171,174)(172,173)(176,247)(177,246)(178,250)(179,249)(180,248)(191,193)(194,195)(196,206)(197,210)(198,209)(199,208)(200,207)(211,215)(212,214)(216,227)(217,226)(218,230)(219,229)(220,228)(231,235)(232,234);;
s2 := (  1,216)(  2,220)(  3,219)(  4,218)(  5,217)(  6,162)(  7,161)(  8,165)(  9,164)( 10,163)( 11,235)( 12,234)( 13,233)( 14,232)( 15,231)( 16,180)( 17,179)( 18,178)( 19,177)( 20,176)( 21,147)( 22,146)( 23,150)( 24,149)( 25,148)( 26,243)( 27,242)( 28,241)( 29,245)( 30,244)( 31,189)( 32,188)( 33,187)( 34,186)( 35,190)( 36,132)( 37,131)( 38,135)( 39,134)( 40,133)( 41,202)( 42,201)( 43,205)( 44,204)( 45,203)( 46,174)( 47,173)( 48,172)( 49,171)( 50,175)( 51,145)( 52,144)( 53,143)( 54,142)( 55,141)( 56,211)( 57,215)( 58,214)( 59,213)( 60,212)( 61,159)( 62,158)( 63,157)( 64,156)( 65,160)( 66,229)( 67,228)( 68,227)( 69,226)( 70,230)( 71,196)( 72,200)( 73,199)( 74,198)( 75,197)( 76,167)( 77,166)( 78,170)( 79,169)( 80,168)( 81,238)( 82,237)( 83,236)( 84,240)( 85,239)( 86,181)( 87,185)( 88,184)( 89,183)( 90,182)( 91,126)( 92,130)( 93,129)( 94,128)( 95,127)( 96,223)( 97,222)( 98,221)( 99,225)(100,224)(101,194)(102,193)(103,192)(104,191)(105,195)(106,140)(107,139)(108,138)(109,137)(110,136)(111,208)(112,207)(113,206)(114,210)(115,209)(116,153)(117,152)(118,151)(119,155)(120,154)(121,250)(122,249)(123,248)(124,247)(125,246);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(250)!(  2,  5)(  3,  4)(  6, 59)(  7, 58)(  8, 57)(  9, 56)( 10, 60)( 11,114)( 12,113)( 13,112)( 14,111)( 15,115)( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21,100)( 22, 99)( 23, 98)( 24, 97)( 25, 96)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31, 34)( 32, 33)( 36, 89)( 37, 88)( 38, 87)( 39, 86)( 40, 90)( 46, 75)( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 61, 64)( 62, 63)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 81,109)( 82,108)( 83,107)( 84,106)( 85,110)( 92, 95)( 93, 94)(121,125)(122,124)(127,130)(128,129)(131,184)(132,183)(133,182)(134,181)(135,185)(136,239)(137,238)(138,237)(139,236)(140,240)(141,166)(142,170)(143,169)(144,168)(145,167)(146,225)(147,224)(148,223)(149,222)(150,221)(151,226)(152,230)(153,229)(154,228)(155,227)(156,159)(157,158)(161,214)(162,213)(163,212)(164,211)(165,215)(171,200)(172,199)(173,198)(174,197)(175,196)(176,201)(177,205)(178,204)(179,203)(180,202)(186,189)(187,188)(191,241)(192,245)(193,244)(194,243)(195,242)(206,234)(207,233)(208,232)(209,231)(210,235)(217,220)(218,219)(246,250)(247,249);
s1 := Sym(250)!(  1,  3)(  4,  5)(  6, 43)(  7, 42)(  8, 41)(  9, 45)( 10, 44)( 11, 56)( 12, 60)( 13, 59)( 14, 58)( 15, 57)( 16, 97)( 17, 96)( 18,100)( 19, 99)( 20, 98)( 21,111)( 22,115)( 23,114)( 24,113)( 25,112)( 26, 63)( 27, 62)( 28, 61)( 29, 65)( 30, 64)( 31, 80)( 32, 79)( 33, 78)( 34, 77)( 35, 76)( 36,120)( 37,119)( 38,118)( 39,117)( 40,116)( 46, 49)( 47, 48)( 51,122)( 52,121)( 53,125)( 54,124)( 55,123)( 66, 68)( 69, 70)( 71, 81)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 86, 90)( 87, 89)( 91,102)( 92,101)( 93,105)( 94,104)( 95,103)(106,110)(107,109)(126,128)(129,130)(131,168)(132,167)(133,166)(134,170)(135,169)(136,181)(137,185)(138,184)(139,183)(140,182)(141,222)(142,221)(143,225)(144,224)(145,223)(146,236)(147,240)(148,239)(149,238)(150,237)(151,188)(152,187)(153,186)(154,190)(155,189)(156,205)(157,204)(158,203)(159,202)(160,201)(161,245)(162,244)(163,243)(164,242)(165,241)(171,174)(172,173)(176,247)(177,246)(178,250)(179,249)(180,248)(191,193)(194,195)(196,206)(197,210)(198,209)(199,208)(200,207)(211,215)(212,214)(216,227)(217,226)(218,230)(219,229)(220,228)(231,235)(232,234);
s2 := Sym(250)!(  1,216)(  2,220)(  3,219)(  4,218)(  5,217)(  6,162)(  7,161)(  8,165)(  9,164)( 10,163)( 11,235)( 12,234)( 13,233)( 14,232)( 15,231)( 16,180)( 17,179)( 18,178)( 19,177)( 20,176)( 21,147)( 22,146)( 23,150)( 24,149)( 25,148)( 26,243)( 27,242)( 28,241)( 29,245)( 30,244)( 31,189)( 32,188)( 33,187)( 34,186)( 35,190)( 36,132)( 37,131)( 38,135)( 39,134)( 40,133)( 41,202)( 42,201)( 43,205)( 44,204)( 45,203)( 46,174)( 47,173)( 48,172)( 49,171)( 50,175)( 51,145)( 52,144)( 53,143)( 54,142)( 55,141)( 56,211)( 57,215)( 58,214)( 59,213)( 60,212)( 61,159)( 62,158)( 63,157)( 64,156)( 65,160)( 66,229)( 67,228)( 68,227)( 69,226)( 70,230)( 71,196)( 72,200)( 73,199)( 74,198)( 75,197)( 76,167)( 77,166)( 78,170)( 79,169)( 80,168)( 81,238)( 82,237)( 83,236)( 84,240)( 85,239)( 86,181)( 87,185)( 88,184)( 89,183)( 90,182)( 91,126)( 92,130)( 93,129)( 94,128)( 95,127)( 96,223)( 97,222)( 98,221)( 99,225)(100,224)(101,194)(102,193)(103,192)(104,191)(105,195)(106,140)(107,139)(108,138)(109,137)(110,136)(111,208)(112,207)(113,206)(114,210)(115,209)(116,153)(117,152)(118,151)(119,155)(120,154)(121,250)(122,249)(123,248)(124,247)(125,246);
poly := sub<Sym(250)|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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.