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