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