Polytope of Type {10,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10}*1000c
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-Dual
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 : {10,10}*500
   5-fold quotients : {10,10}*200a
   25-fold quotients : {2,10}*40, {10,2}*40
   50-fold quotients : {2,5}*20, {5,2}*20
   125-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,20}*2000b, {20,10}*2000b
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)(  2,155)(  3,154)(  4,153)(  5,152)(  6,157)(  7,156)(  8,160)
(  9,159)( 10,158)( 11,163)( 12,162)( 13,161)( 14,165)( 15,164)( 16,169)
( 17,168)( 18,167)( 19,166)( 20,170)( 21,175)( 22,174)( 23,173)( 24,172)
( 25,171)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,132)( 32,131)
( 33,135)( 34,134)( 35,133)( 36,138)( 37,137)( 38,136)( 39,140)( 40,139)
( 41,144)( 42,143)( 43,142)( 44,141)( 45,145)( 46,150)( 47,149)( 48,148)
( 49,147)( 50,146)( 51,226)( 52,230)( 53,229)( 54,228)( 55,227)( 56,232)
( 57,231)( 58,235)( 59,234)( 60,233)( 61,238)( 62,237)( 63,236)( 64,240)
( 65,239)( 66,244)( 67,243)( 68,242)( 69,241)( 70,245)( 71,250)( 72,249)
( 73,248)( 74,247)( 75,246)( 76,201)( 77,205)( 78,204)( 79,203)( 80,202)
( 81,207)( 82,206)( 83,210)( 84,209)( 85,208)( 86,213)( 87,212)( 88,211)
( 89,215)( 90,214)( 91,219)( 92,218)( 93,217)( 94,216)( 95,220)( 96,225)
( 97,224)( 98,223)( 99,222)(100,221)(101,176)(102,180)(103,179)(104,178)
(105,177)(106,182)(107,181)(108,185)(109,184)(110,183)(111,188)(112,187)
(113,186)(114,190)(115,189)(116,194)(117,193)(118,192)(119,191)(120,195)
(121,200)(122,199)(123,198)(124,197)(125,196);;
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*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, 
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)(  2,155)(  3,154)(  4,153)(  5,152)(  6,157)(  7,156)
(  8,160)(  9,159)( 10,158)( 11,163)( 12,162)( 13,161)( 14,165)( 15,164)
( 16,169)( 17,168)( 18,167)( 19,166)( 20,170)( 21,175)( 22,174)( 23,173)
( 24,172)( 25,171)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,132)
( 32,131)( 33,135)( 34,134)( 35,133)( 36,138)( 37,137)( 38,136)( 39,140)
( 40,139)( 41,144)( 42,143)( 43,142)( 44,141)( 45,145)( 46,150)( 47,149)
( 48,148)( 49,147)( 50,146)( 51,226)( 52,230)( 53,229)( 54,228)( 55,227)
( 56,232)( 57,231)( 58,235)( 59,234)( 60,233)( 61,238)( 62,237)( 63,236)
( 64,240)( 65,239)( 66,244)( 67,243)( 68,242)( 69,241)( 70,245)( 71,250)
( 72,249)( 73,248)( 74,247)( 75,246)( 76,201)( 77,205)( 78,204)( 79,203)
( 80,202)( 81,207)( 82,206)( 83,210)( 84,209)( 85,208)( 86,213)( 87,212)
( 88,211)( 89,215)( 90,214)( 91,219)( 92,218)( 93,217)( 94,216)( 95,220)
( 96,225)( 97,224)( 98,223)( 99,222)(100,221)(101,176)(102,180)(103,179)
(104,178)(105,177)(106,182)(107,181)(108,185)(109,184)(110,183)(111,188)
(112,187)(113,186)(114,190)(115,189)(116,194)(117,193)(118,192)(119,191)
(120,195)(121,200)(122,199)(123,198)(124,197)(125,196);
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*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, 
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