Polytope of Type {20,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,10}*2000j
if this polytope has a name.
Group : SmallGroup(2000,942)
Rank : 3
Schlafli Type : {20,10}
Number of vertices, edges, etc : 100, 500, 50
Order of s0s1s2 : 20
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {20,10}*1000e
5-fold quotients : {4,10}*400
10-fold quotients : {4,10}*200
25-fold quotients : {20,2}*80
50-fold quotients : {10,2}*40
100-fold quotients : {5,2}*20
125-fold quotients : {4,2}*16
250-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 6, 56)( 7, 60)( 8, 59)( 9, 58)( 10, 57)( 11,111)
( 12,115)( 13,114)( 14,113)( 15,112)( 16, 41)( 17, 45)( 18, 44)( 19, 43)
( 20, 42)( 21, 96)( 22,100)( 23, 99)( 24, 98)( 25, 97)( 26,101)( 27,105)
( 28,104)( 29,103)( 30,102)( 32, 35)( 33, 34)( 36, 86)( 37, 90)( 38, 89)
( 39, 88)( 40, 87)( 46, 71)( 47, 75)( 48, 74)( 49, 73)( 50, 72)( 51, 76)
( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 62, 65)( 63, 64)( 66,116)( 67,120)
( 68,119)( 69,118)( 70,117)( 81,106)( 82,110)( 83,109)( 84,108)( 85,107)
( 92, 95)( 93, 94)(122,125)(123,124)(127,130)(128,129)(131,181)(132,185)
(133,184)(134,183)(135,182)(136,236)(137,240)(138,239)(139,238)(140,237)
(141,166)(142,170)(143,169)(144,168)(145,167)(146,221)(147,225)(148,224)
(149,223)(150,222)(151,226)(152,230)(153,229)(154,228)(155,227)(157,160)
(158,159)(161,211)(162,215)(163,214)(164,213)(165,212)(171,196)(172,200)
(173,199)(174,198)(175,197)(176,201)(177,205)(178,204)(179,203)(180,202)
(187,190)(188,189)(191,241)(192,245)(193,244)(194,243)(195,242)(206,231)
(207,235)(208,234)(209,233)(210,232)(217,220)(218,219)(247,250)(248,249);;
s1 := ( 1, 2)( 3, 5)( 6, 42)( 7, 41)( 8, 45)( 9, 44)( 10, 43)( 11, 57)
( 12, 56)( 13, 60)( 14, 59)( 15, 58)( 16, 97)( 17, 96)( 18,100)( 19, 99)
( 20, 98)( 21,112)( 22,111)( 23,115)( 24,114)( 25,113)( 26, 62)( 27, 61)
( 28, 65)( 29, 64)( 30, 63)( 31, 77)( 32, 76)( 33, 80)( 34, 79)( 35, 78)
( 36,117)( 37,116)( 38,120)( 39,119)( 40,118)( 46, 47)( 48, 50)( 51,122)
( 52,121)( 53,125)( 54,124)( 55,123)( 66, 67)( 68, 70)( 71, 82)( 72, 81)
( 73, 85)( 74, 84)( 75, 83)( 86, 87)( 88, 90)( 91,102)( 92,101)( 93,105)
( 94,104)( 95,103)(106,107)(108,110)(126,127)(128,130)(131,167)(132,166)
(133,170)(134,169)(135,168)(136,182)(137,181)(138,185)(139,184)(140,183)
(141,222)(142,221)(143,225)(144,224)(145,223)(146,237)(147,236)(148,240)
(149,239)(150,238)(151,187)(152,186)(153,190)(154,189)(155,188)(156,202)
(157,201)(158,205)(159,204)(160,203)(161,242)(162,241)(163,245)(164,244)
(165,243)(171,172)(173,175)(176,247)(177,246)(178,250)(179,249)(180,248)
(191,192)(193,195)(196,207)(197,206)(198,210)(199,209)(200,208)(211,212)
(213,215)(216,227)(217,226)(218,230)(219,229)(220,228)(231,232)(233,235);;
s2 := ( 1,156)( 2,157)( 3,158)( 4,159)( 5,160)( 6,151)( 7,152)( 8,153)
( 9,154)( 10,155)( 11,171)( 12,172)( 13,173)( 14,174)( 15,175)( 16,166)
( 17,167)( 18,168)( 19,169)( 20,170)( 21,161)( 22,162)( 23,163)( 24,164)
( 25,165)( 26,131)( 27,132)( 28,133)( 29,134)( 30,135)( 31,126)( 32,127)
( 33,128)( 34,129)( 35,130)( 36,146)( 37,147)( 38,148)( 39,149)( 40,150)
( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,136)( 47,137)( 48,138)
( 49,139)( 50,140)( 51,231)( 52,232)( 53,233)( 54,234)( 55,235)( 56,226)
( 57,227)( 58,228)( 59,229)( 60,230)( 61,246)( 62,247)( 63,248)( 64,249)
( 65,250)( 66,241)( 67,242)( 68,243)( 69,244)( 70,245)( 71,236)( 72,237)
( 73,238)( 74,239)( 75,240)( 76,206)( 77,207)( 78,208)( 79,209)( 80,210)
( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,221)( 87,222)( 88,223)
( 89,224)( 90,225)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)( 96,211)
( 97,212)( 98,213)( 99,214)(100,215)(101,181)(102,182)(103,183)(104,184)
(105,185)(106,176)(107,177)(108,178)(109,179)(110,180)(111,196)(112,197)
(113,198)(114,199)(115,200)(116,191)(117,192)(118,193)(119,194)(120,195)
(121,186)(122,187)(123,188)(124,189)(125,190);;
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*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(250)!( 2, 5)( 3, 4)( 6, 56)( 7, 60)( 8, 59)( 9, 58)( 10, 57)
( 11,111)( 12,115)( 13,114)( 14,113)( 15,112)( 16, 41)( 17, 45)( 18, 44)
( 19, 43)( 20, 42)( 21, 96)( 22,100)( 23, 99)( 24, 98)( 25, 97)( 26,101)
( 27,105)( 28,104)( 29,103)( 30,102)( 32, 35)( 33, 34)( 36, 86)( 37, 90)
( 38, 89)( 39, 88)( 40, 87)( 46, 71)( 47, 75)( 48, 74)( 49, 73)( 50, 72)
( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 62, 65)( 63, 64)( 66,116)
( 67,120)( 68,119)( 69,118)( 70,117)( 81,106)( 82,110)( 83,109)( 84,108)
( 85,107)( 92, 95)( 93, 94)(122,125)(123,124)(127,130)(128,129)(131,181)
(132,185)(133,184)(134,183)(135,182)(136,236)(137,240)(138,239)(139,238)
(140,237)(141,166)(142,170)(143,169)(144,168)(145,167)(146,221)(147,225)
(148,224)(149,223)(150,222)(151,226)(152,230)(153,229)(154,228)(155,227)
(157,160)(158,159)(161,211)(162,215)(163,214)(164,213)(165,212)(171,196)
(172,200)(173,199)(174,198)(175,197)(176,201)(177,205)(178,204)(179,203)
(180,202)(187,190)(188,189)(191,241)(192,245)(193,244)(194,243)(195,242)
(206,231)(207,235)(208,234)(209,233)(210,232)(217,220)(218,219)(247,250)
(248,249);
s1 := Sym(250)!( 1, 2)( 3, 5)( 6, 42)( 7, 41)( 8, 45)( 9, 44)( 10, 43)
( 11, 57)( 12, 56)( 13, 60)( 14, 59)( 15, 58)( 16, 97)( 17, 96)( 18,100)
( 19, 99)( 20, 98)( 21,112)( 22,111)( 23,115)( 24,114)( 25,113)( 26, 62)
( 27, 61)( 28, 65)( 29, 64)( 30, 63)( 31, 77)( 32, 76)( 33, 80)( 34, 79)
( 35, 78)( 36,117)( 37,116)( 38,120)( 39,119)( 40,118)( 46, 47)( 48, 50)
( 51,122)( 52,121)( 53,125)( 54,124)( 55,123)( 66, 67)( 68, 70)( 71, 82)
( 72, 81)( 73, 85)( 74, 84)( 75, 83)( 86, 87)( 88, 90)( 91,102)( 92,101)
( 93,105)( 94,104)( 95,103)(106,107)(108,110)(126,127)(128,130)(131,167)
(132,166)(133,170)(134,169)(135,168)(136,182)(137,181)(138,185)(139,184)
(140,183)(141,222)(142,221)(143,225)(144,224)(145,223)(146,237)(147,236)
(148,240)(149,239)(150,238)(151,187)(152,186)(153,190)(154,189)(155,188)
(156,202)(157,201)(158,205)(159,204)(160,203)(161,242)(162,241)(163,245)
(164,244)(165,243)(171,172)(173,175)(176,247)(177,246)(178,250)(179,249)
(180,248)(191,192)(193,195)(196,207)(197,206)(198,210)(199,209)(200,208)
(211,212)(213,215)(216,227)(217,226)(218,230)(219,229)(220,228)(231,232)
(233,235);
s2 := Sym(250)!( 1,156)( 2,157)( 3,158)( 4,159)( 5,160)( 6,151)( 7,152)
( 8,153)( 9,154)( 10,155)( 11,171)( 12,172)( 13,173)( 14,174)( 15,175)
( 16,166)( 17,167)( 18,168)( 19,169)( 20,170)( 21,161)( 22,162)( 23,163)
( 24,164)( 25,165)( 26,131)( 27,132)( 28,133)( 29,134)( 30,135)( 31,126)
( 32,127)( 33,128)( 34,129)( 35,130)( 36,146)( 37,147)( 38,148)( 39,149)
( 40,150)( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,136)( 47,137)
( 48,138)( 49,139)( 50,140)( 51,231)( 52,232)( 53,233)( 54,234)( 55,235)
( 56,226)( 57,227)( 58,228)( 59,229)( 60,230)( 61,246)( 62,247)( 63,248)
( 64,249)( 65,250)( 66,241)( 67,242)( 68,243)( 69,244)( 70,245)( 71,236)
( 72,237)( 73,238)( 74,239)( 75,240)( 76,206)( 77,207)( 78,208)( 79,209)
( 80,210)( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,221)( 87,222)
( 88,223)( 89,224)( 90,225)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)
( 96,211)( 97,212)( 98,213)( 99,214)(100,215)(101,181)(102,182)(103,183)
(104,184)(105,185)(106,176)(107,177)(108,178)(109,179)(110,180)(111,196)
(112,197)(113,198)(114,199)(115,200)(116,191)(117,192)(118,193)(119,194)
(120,195)(121,186)(122,187)(123,188)(124,189)(125,190);
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, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope