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Polytope of Type {10,50}

Atlas Canonical Name : {10,50}*1000a
Also Known As : {10,50|2}. if this polytope has another name.
Group : SmallGroup(1000,105)
Rank : 3
Schlafli Type : {10,50}
Number of vertices, edges, etc : 10, 250, 50
Order of s0s1s2 : 50
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,50,2} of size 2000
Vertex Figure Of :
{2,10,50} of size 2000
Quotients (Maximal Quotients in Boldface) :
5-fold quotients : {2,50}*200, {10,10}*200a
10-fold quotients : {2,25}*100
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 : {20,50}*2000a, {10,100}*2000a
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)( 26,110)( 27,109)( 28,108)( 29,107)
( 30,106)( 31,105)( 32,104)( 33,103)( 34,102)( 35,101)( 36,125)( 37,124)
( 38,123)( 39,122)( 40,121)( 41,120)( 42,119)( 43,118)( 44,117)( 45,116)
( 46,115)( 47,114)( 48,113)( 49,112)( 50,111)( 51, 85)( 52, 84)( 53, 83)
( 54, 82)( 55, 81)( 56, 80)( 57, 79)( 58, 78)( 59, 77)( 60, 76)( 61,100)
( 62, 99)( 63, 98)( 64, 97)( 65, 96)( 66, 95)( 67, 94)( 68, 93)( 69, 92)
( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)(126,131)(127,135)
(128,134)(129,133)(130,132)(136,146)(137,150)(138,149)(139,148)(140,147)
(142,145)(143,144)(151,235)(152,234)(153,233)(154,232)(155,231)(156,230)
(157,229)(158,228)(159,227)(160,226)(161,250)(162,249)(163,248)(164,247)
(165,246)(166,245)(167,244)(168,243)(169,242)(170,241)(171,240)(172,239)
(173,238)(174,237)(175,236)(176,210)(177,209)(178,208)(179,207)(180,206)
(181,205)(182,204)(183,203)(184,202)(185,201)(186,225)(187,224)(188,223)
(189,222)(190,221)(191,220)(192,219)(193,218)(194,217)(195,216)(196,215)
(197,214)(198,213)(199,212)(200,211);;
s2 := (  1,151)(  2,155)(  3,154)(  4,153)(  5,152)(  6,156)(  7,160)(  8,159)
(  9,158)( 10,157)( 11,161)( 12,165)( 13,164)( 14,163)( 15,162)( 16,166)
( 17,170)( 18,169)( 19,168)( 20,167)( 21,171)( 22,175)( 23,174)( 24,173)
( 25,172)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,131)( 32,135)
( 33,134)( 34,133)( 35,132)( 36,136)( 37,140)( 38,139)( 39,138)( 40,137)
( 41,141)( 42,145)( 43,144)( 44,143)( 45,142)( 46,146)( 47,150)( 48,149)
( 49,148)( 50,147)( 51,230)( 52,229)( 53,228)( 54,227)( 55,226)( 56,235)
( 57,234)( 58,233)( 59,232)( 60,231)( 61,240)( 62,239)( 63,238)( 64,237)
( 65,236)( 66,245)( 67,244)( 68,243)( 69,242)( 70,241)( 71,250)( 72,249)
( 73,248)( 74,247)( 75,246)( 76,205)( 77,204)( 78,203)( 79,202)( 80,201)
( 81,210)( 82,209)( 83,208)( 84,207)( 85,206)( 86,215)( 87,214)( 88,213)
( 89,212)( 90,211)( 91,220)( 92,219)( 93,218)( 94,217)( 95,216)( 96,225)
( 97,224)( 98,223)( 99,222)(100,221)(101,180)(102,179)(103,178)(104,177)
(105,176)(106,185)(107,184)(108,183)(109,182)(110,181)(111,190)(112,189)
(113,188)(114,187)(115,186)(116,195)(117,194)(118,193)(119,192)(120,191)
(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,
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!(  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)( 26,110)( 27,109)( 28,108)
( 29,107)( 30,106)( 31,105)( 32,104)( 33,103)( 34,102)( 35,101)( 36,125)
( 37,124)( 38,123)( 39,122)( 40,121)( 41,120)( 42,119)( 43,118)( 44,117)
( 45,116)( 46,115)( 47,114)( 48,113)( 49,112)( 50,111)( 51, 85)( 52, 84)
( 53, 83)( 54, 82)( 55, 81)( 56, 80)( 57, 79)( 58, 78)( 59, 77)( 60, 76)
( 61,100)( 62, 99)( 63, 98)( 64, 97)( 65, 96)( 66, 95)( 67, 94)( 68, 93)
( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)(126,131)
(127,135)(128,134)(129,133)(130,132)(136,146)(137,150)(138,149)(139,148)
(140,147)(142,145)(143,144)(151,235)(152,234)(153,233)(154,232)(155,231)
(156,230)(157,229)(158,228)(159,227)(160,226)(161,250)(162,249)(163,248)
(164,247)(165,246)(166,245)(167,244)(168,243)(169,242)(170,241)(171,240)
(172,239)(173,238)(174,237)(175,236)(176,210)(177,209)(178,208)(179,207)
(180,206)(181,205)(182,204)(183,203)(184,202)(185,201)(186,225)(187,224)
(188,223)(189,222)(190,221)(191,220)(192,219)(193,218)(194,217)(195,216)
(196,215)(197,214)(198,213)(199,212)(200,211);
s2 := Sym(250)!(  1,151)(  2,155)(  3,154)(  4,153)(  5,152)(  6,156)(  7,160)
(  8,159)(  9,158)( 10,157)( 11,161)( 12,165)( 13,164)( 14,163)( 15,162)
( 16,166)( 17,170)( 18,169)( 19,168)( 20,167)( 21,171)( 22,175)( 23,174)
( 24,173)( 25,172)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,131)
( 32,135)( 33,134)( 34,133)( 35,132)( 36,136)( 37,140)( 38,139)( 39,138)
( 40,137)( 41,141)( 42,145)( 43,144)( 44,143)( 45,142)( 46,146)( 47,150)
( 48,149)( 49,148)( 50,147)( 51,230)( 52,229)( 53,228)( 54,227)( 55,226)
( 56,235)( 57,234)( 58,233)( 59,232)( 60,231)( 61,240)( 62,239)( 63,238)
( 64,237)( 65,236)( 66,245)( 67,244)( 68,243)( 69,242)( 70,241)( 71,250)
( 72,249)( 73,248)( 74,247)( 75,246)( 76,205)( 77,204)( 78,203)( 79,202)
( 80,201)( 81,210)( 82,209)( 83,208)( 84,207)( 85,206)( 86,215)( 87,214)
( 88,213)( 89,212)( 90,211)( 91,220)( 92,219)( 93,218)( 94,217)( 95,216)
( 96,225)( 97,224)( 98,223)( 99,222)(100,221)(101,180)(102,179)(103,178)
(104,177)(105,176)(106,185)(107,184)(108,183)(109,182)(110,181)(111,190)
(112,189)(113,188)(114,187)(115,186)(116,195)(117,194)(118,193)(119,192)
(120,191)(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,
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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