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