Polytope of Type {10,10,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10,10}*2000f
if this polytope has a name.
Group : SmallGroup(2000,946)
Rank : 4
Schlafli Type : {10,10,10}
Number of vertices, edges, etc : 10, 50, 50, 10
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,5,10}*1000
5-fold quotients : {2,10,10}*400c, {10,10,2}*400b
10-fold quotients : {2,5,10}*200, {10,5,2}*200
25-fold quotients : {2,10,2}*80
50-fold quotients : {2,5,2}*40
125-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)( 59, 74)
( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)
( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)
(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)
(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)
(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)(159,174)
(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)(182,197)
(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)(190,195)
(206,221)(207,222)(208,223)(209,224)(210,225)(211,216)(212,217)(213,218)
(214,219)(215,220)(231,246)(232,247)(233,248)(234,249)(235,250)(236,241)
(237,242)(238,243)(239,244)(240,245);;
s1 := ( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 21)( 12, 25)( 13, 24)
( 14, 23)( 15, 22)( 17, 20)( 18, 19)( 26,106)( 27,110)( 28,109)( 29,108)
( 30,107)( 31,101)( 32,105)( 33,104)( 34,103)( 35,102)( 36,121)( 37,125)
( 38,124)( 39,123)( 40,122)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)
( 46,111)( 47,115)( 48,114)( 49,113)( 50,112)( 51, 81)( 52, 85)( 53, 84)
( 54, 83)( 55, 82)( 56, 76)( 57, 80)( 58, 79)( 59, 78)( 60, 77)( 61, 96)
( 62,100)( 63, 99)( 64, 98)( 65, 97)( 66, 91)( 67, 95)( 68, 94)( 69, 93)
( 70, 92)( 71, 86)( 72, 90)( 73, 89)( 74, 88)( 75, 87)(126,131)(127,135)
(128,134)(129,133)(130,132)(136,146)(137,150)(138,149)(139,148)(140,147)
(142,145)(143,144)(151,231)(152,235)(153,234)(154,233)(155,232)(156,226)
(157,230)(158,229)(159,228)(160,227)(161,246)(162,250)(163,249)(164,248)
(165,247)(166,241)(167,245)(168,244)(169,243)(170,242)(171,236)(172,240)
(173,239)(174,238)(175,237)(176,206)(177,210)(178,209)(179,208)(180,207)
(181,201)(182,205)(183,204)(184,203)(185,202)(186,221)(187,225)(188,224)
(189,223)(190,222)(191,216)(192,220)(193,219)(194,218)(195,217)(196,211)
(197,215)(198,214)(199,213)(200,212);;
s2 := ( 1,152)( 2,151)( 3,155)( 4,154)( 5,153)( 6,172)( 7,171)( 8,175)
( 9,174)( 10,173)( 11,167)( 12,166)( 13,170)( 14,169)( 15,168)( 16,162)
( 17,161)( 18,165)( 19,164)( 20,163)( 21,157)( 22,156)( 23,160)( 24,159)
( 25,158)( 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)( 51,227)( 52,226)( 53,230)( 54,229)( 55,228)( 56,247)
( 57,246)( 58,250)( 59,249)( 60,248)( 61,242)( 62,241)( 63,245)( 64,244)
( 65,243)( 66,237)( 67,236)( 68,240)( 69,239)( 70,238)( 71,232)( 72,231)
( 73,235)( 74,234)( 75,233)( 76,202)( 77,201)( 78,205)( 79,204)( 80,203)
( 81,222)( 82,221)( 83,225)( 84,224)( 85,223)( 86,217)( 87,216)( 88,220)
( 89,219)( 90,218)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)( 96,207)
( 97,206)( 98,210)( 99,209)(100,208)(101,177)(102,176)(103,180)(104,179)
(105,178)(106,197)(107,196)(108,200)(109,199)(110,198)(111,192)(112,191)
(113,195)(114,194)(115,193)(116,187)(117,186)(118,190)(119,189)(120,188)
(121,182)(122,181)(123,185)(124,184)(125,183);;
s3 := ( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)( 31,106)( 32,107)( 33,108)
( 34,109)( 35,110)( 36,111)( 37,112)( 38,113)( 39,114)( 40,115)( 41,116)
( 42,117)( 43,118)( 44,119)( 45,120)( 46,121)( 47,122)( 48,123)( 49,124)
( 50,125)( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)
( 58, 83)( 59, 84)( 60, 85)( 61, 86)( 62, 87)( 63, 88)( 64, 89)( 65, 90)
( 66, 91)( 67, 92)( 68, 93)( 69, 94)( 70, 95)( 71, 96)( 72, 97)( 73, 98)
( 74, 99)( 75,100)(151,226)(152,227)(153,228)(154,229)(155,230)(156,231)
(157,232)(158,233)(159,234)(160,235)(161,236)(162,237)(163,238)(164,239)
(165,240)(166,241)(167,242)(168,243)(169,244)(170,245)(171,246)(172,247)
(173,248)(174,249)(175,250)(176,201)(177,202)(178,203)(179,204)(180,205)
(181,206)(182,207)(183,208)(184,209)(185,210)(186,211)(187,212)(188,213)
(189,214)(190,215)(191,216)(192,217)(193,218)(194,219)(195,220)(196,221)
(197,222)(198,223)(199,224)(200,225);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 ];;
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)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)
( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)
( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)
( 90, 95)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)
(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)
(136,141)(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)
(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)
(182,197)(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)
(190,195)(206,221)(207,222)(208,223)(209,224)(210,225)(211,216)(212,217)
(213,218)(214,219)(215,220)(231,246)(232,247)(233,248)(234,249)(235,250)
(236,241)(237,242)(238,243)(239,244)(240,245);
s1 := Sym(250)!( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 21)( 12, 25)
( 13, 24)( 14, 23)( 15, 22)( 17, 20)( 18, 19)( 26,106)( 27,110)( 28,109)
( 29,108)( 30,107)( 31,101)( 32,105)( 33,104)( 34,103)( 35,102)( 36,121)
( 37,125)( 38,124)( 39,123)( 40,122)( 41,116)( 42,120)( 43,119)( 44,118)
( 45,117)( 46,111)( 47,115)( 48,114)( 49,113)( 50,112)( 51, 81)( 52, 85)
( 53, 84)( 54, 83)( 55, 82)( 56, 76)( 57, 80)( 58, 79)( 59, 78)( 60, 77)
( 61, 96)( 62,100)( 63, 99)( 64, 98)( 65, 97)( 66, 91)( 67, 95)( 68, 94)
( 69, 93)( 70, 92)( 71, 86)( 72, 90)( 73, 89)( 74, 88)( 75, 87)(126,131)
(127,135)(128,134)(129,133)(130,132)(136,146)(137,150)(138,149)(139,148)
(140,147)(142,145)(143,144)(151,231)(152,235)(153,234)(154,233)(155,232)
(156,226)(157,230)(158,229)(159,228)(160,227)(161,246)(162,250)(163,249)
(164,248)(165,247)(166,241)(167,245)(168,244)(169,243)(170,242)(171,236)
(172,240)(173,239)(174,238)(175,237)(176,206)(177,210)(178,209)(179,208)
(180,207)(181,201)(182,205)(183,204)(184,203)(185,202)(186,221)(187,225)
(188,224)(189,223)(190,222)(191,216)(192,220)(193,219)(194,218)(195,217)
(196,211)(197,215)(198,214)(199,213)(200,212);
s2 := Sym(250)!( 1,152)( 2,151)( 3,155)( 4,154)( 5,153)( 6,172)( 7,171)
( 8,175)( 9,174)( 10,173)( 11,167)( 12,166)( 13,170)( 14,169)( 15,168)
( 16,162)( 17,161)( 18,165)( 19,164)( 20,163)( 21,157)( 22,156)( 23,160)
( 24,159)( 25,158)( 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)( 51,227)( 52,226)( 53,230)( 54,229)( 55,228)
( 56,247)( 57,246)( 58,250)( 59,249)( 60,248)( 61,242)( 62,241)( 63,245)
( 64,244)( 65,243)( 66,237)( 67,236)( 68,240)( 69,239)( 70,238)( 71,232)
( 72,231)( 73,235)( 74,234)( 75,233)( 76,202)( 77,201)( 78,205)( 79,204)
( 80,203)( 81,222)( 82,221)( 83,225)( 84,224)( 85,223)( 86,217)( 87,216)
( 88,220)( 89,219)( 90,218)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)
( 96,207)( 97,206)( 98,210)( 99,209)(100,208)(101,177)(102,176)(103,180)
(104,179)(105,178)(106,197)(107,196)(108,200)(109,199)(110,198)(111,192)
(112,191)(113,195)(114,194)(115,193)(116,187)(117,186)(118,190)(119,189)
(120,188)(121,182)(122,181)(123,185)(124,184)(125,183);
s3 := Sym(250)!( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)( 31,106)( 32,107)
( 33,108)( 34,109)( 35,110)( 36,111)( 37,112)( 38,113)( 39,114)( 40,115)
( 41,116)( 42,117)( 43,118)( 44,119)( 45,120)( 46,121)( 47,122)( 48,123)
( 49,124)( 50,125)( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56, 81)
( 57, 82)( 58, 83)( 59, 84)( 60, 85)( 61, 86)( 62, 87)( 63, 88)( 64, 89)
( 65, 90)( 66, 91)( 67, 92)( 68, 93)( 69, 94)( 70, 95)( 71, 96)( 72, 97)
( 73, 98)( 74, 99)( 75,100)(151,226)(152,227)(153,228)(154,229)(155,230)
(156,231)(157,232)(158,233)(159,234)(160,235)(161,236)(162,237)(163,238)
(164,239)(165,240)(166,241)(167,242)(168,243)(169,244)(170,245)(171,246)
(172,247)(173,248)(174,249)(175,250)(176,201)(177,202)(178,203)(179,204)
(180,205)(181,206)(182,207)(183,208)(184,209)(185,210)(186,211)(187,212)
(188,213)(189,214)(190,215)(191,216)(192,217)(193,218)(194,219)(195,220)
(196,221)(197,222)(198,223)(199,224)(200,225);
poly := sub<Sym(250)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope