Polytope of Type {2,10,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,10}*2000c
if this polytope has a name.
Group : SmallGroup(2000,501)
Rank : 4
Schlafli Type : {2,10,10}
Number of vertices, edges, etc : 2, 50, 250, 50
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
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 : {2,10,10}*1000
5-fold quotients : {2,10,10}*400a
25-fold quotients : {2,2,10}*80, {2,10,2}*80
50-fold quotients : {2,2,5}*40, {2,5,2}*40
125-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 8, 23)( 9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 18)
( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 29, 32)( 30, 31)( 33, 48)( 34, 52)
( 35, 51)( 36, 50)( 37, 49)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)
( 54, 57)( 55, 56)( 58, 73)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 68)
( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 79, 82)( 80, 81)( 83, 98)( 84,102)
( 85,101)( 86,100)( 87, 99)( 88, 93)( 89, 97)( 90, 96)( 91, 95)( 92, 94)
(104,107)(105,106)(108,123)(109,127)(110,126)(111,125)(112,124)(113,118)
(114,122)(115,121)(116,120)(117,119)(129,132)(130,131)(133,148)(134,152)
(135,151)(136,150)(137,149)(138,143)(139,147)(140,146)(141,145)(142,144)
(154,157)(155,156)(158,173)(159,177)(160,176)(161,175)(162,174)(163,168)
(164,172)(165,171)(166,170)(167,169)(179,182)(180,181)(183,198)(184,202)
(185,201)(186,200)(187,199)(188,193)(189,197)(190,196)(191,195)(192,194)
(204,207)(205,206)(208,223)(209,227)(210,226)(211,225)(212,224)(213,218)
(214,222)(215,221)(216,220)(217,219)(229,232)(230,231)(233,248)(234,252)
(235,251)(236,250)(237,249)(238,243)(239,247)(240,246)(241,245)(242,244);;
s2 := ( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 13, 23)( 14, 24)( 15, 25)
( 16, 26)( 17, 27)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)( 33,103)
( 34,104)( 35,105)( 36,106)( 37,107)( 38,123)( 39,124)( 40,125)( 41,126)
( 42,127)( 43,118)( 44,119)( 45,120)( 46,121)( 47,122)( 48,113)( 49,114)
( 50,115)( 51,116)( 52,117)( 53, 83)( 54, 84)( 55, 85)( 56, 86)( 57, 87)
( 58, 78)( 59, 79)( 60, 80)( 61, 81)( 62, 82)( 63, 98)( 64, 99)( 65,100)
( 66,101)( 67,102)( 68, 93)( 69, 94)( 70, 95)( 71, 96)( 72, 97)( 73, 88)
( 74, 89)( 75, 90)( 76, 91)( 77, 92)(128,133)(129,134)(130,135)(131,136)
(132,137)(138,148)(139,149)(140,150)(141,151)(142,152)(153,233)(154,234)
(155,235)(156,236)(157,237)(158,228)(159,229)(160,230)(161,231)(162,232)
(163,248)(164,249)(165,250)(166,251)(167,252)(168,243)(169,244)(170,245)
(171,246)(172,247)(173,238)(174,239)(175,240)(176,241)(177,242)(178,208)
(179,209)(180,210)(181,211)(182,212)(183,203)(184,204)(185,205)(186,206)
(187,207)(188,223)(189,224)(190,225)(191,226)(192,227)(193,218)(194,219)
(195,220)(196,221)(197,222)(198,213)(199,214)(200,215)(201,216)(202,217);;
s3 := ( 3,153)( 4,157)( 5,156)( 6,155)( 7,154)( 8,159)( 9,158)( 10,162)
( 11,161)( 12,160)( 13,165)( 14,164)( 15,163)( 16,167)( 17,166)( 18,171)
( 19,170)( 20,169)( 21,168)( 22,172)( 23,177)( 24,176)( 25,175)( 26,174)
( 27,173)( 28,128)( 29,132)( 30,131)( 31,130)( 32,129)( 33,134)( 34,133)
( 35,137)( 36,136)( 37,135)( 38,140)( 39,139)( 40,138)( 41,142)( 42,141)
( 43,146)( 44,145)( 45,144)( 46,143)( 47,147)( 48,152)( 49,151)( 50,150)
( 51,149)( 52,148)( 53,228)( 54,232)( 55,231)( 56,230)( 57,229)( 58,234)
( 59,233)( 60,237)( 61,236)( 62,235)( 63,240)( 64,239)( 65,238)( 66,242)
( 67,241)( 68,246)( 69,245)( 70,244)( 71,243)( 72,247)( 73,252)( 74,251)
( 75,250)( 76,249)( 77,248)( 78,203)( 79,207)( 80,206)( 81,205)( 82,204)
( 83,209)( 84,208)( 85,212)( 86,211)( 87,210)( 88,215)( 89,214)( 90,213)
( 91,217)( 92,216)( 93,221)( 94,220)( 95,219)( 96,218)( 97,222)( 98,227)
( 99,226)(100,225)(101,224)(102,223)(103,178)(104,182)(105,181)(106,180)
(107,179)(108,184)(109,183)(110,187)(111,186)(112,185)(113,190)(114,189)
(115,188)(116,192)(117,191)(118,196)(119,195)(120,194)(121,193)(122,197)
(123,202)(124,201)(125,200)(126,199)(127,198);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2,
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(252)!(1,2);
s1 := Sym(252)!( 4, 7)( 5, 6)( 8, 23)( 9, 27)( 10, 26)( 11, 25)( 12, 24)
( 13, 18)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 29, 32)( 30, 31)( 33, 48)
( 34, 52)( 35, 51)( 36, 50)( 37, 49)( 38, 43)( 39, 47)( 40, 46)( 41, 45)
( 42, 44)( 54, 57)( 55, 56)( 58, 73)( 59, 77)( 60, 76)( 61, 75)( 62, 74)
( 63, 68)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 79, 82)( 80, 81)( 83, 98)
( 84,102)( 85,101)( 86,100)( 87, 99)( 88, 93)( 89, 97)( 90, 96)( 91, 95)
( 92, 94)(104,107)(105,106)(108,123)(109,127)(110,126)(111,125)(112,124)
(113,118)(114,122)(115,121)(116,120)(117,119)(129,132)(130,131)(133,148)
(134,152)(135,151)(136,150)(137,149)(138,143)(139,147)(140,146)(141,145)
(142,144)(154,157)(155,156)(158,173)(159,177)(160,176)(161,175)(162,174)
(163,168)(164,172)(165,171)(166,170)(167,169)(179,182)(180,181)(183,198)
(184,202)(185,201)(186,200)(187,199)(188,193)(189,197)(190,196)(191,195)
(192,194)(204,207)(205,206)(208,223)(209,227)(210,226)(211,225)(212,224)
(213,218)(214,222)(215,221)(216,220)(217,219)(229,232)(230,231)(233,248)
(234,252)(235,251)(236,250)(237,249)(238,243)(239,247)(240,246)(241,245)
(242,244);
s2 := Sym(252)!( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 13, 23)( 14, 24)
( 15, 25)( 16, 26)( 17, 27)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)
( 33,103)( 34,104)( 35,105)( 36,106)( 37,107)( 38,123)( 39,124)( 40,125)
( 41,126)( 42,127)( 43,118)( 44,119)( 45,120)( 46,121)( 47,122)( 48,113)
( 49,114)( 50,115)( 51,116)( 52,117)( 53, 83)( 54, 84)( 55, 85)( 56, 86)
( 57, 87)( 58, 78)( 59, 79)( 60, 80)( 61, 81)( 62, 82)( 63, 98)( 64, 99)
( 65,100)( 66,101)( 67,102)( 68, 93)( 69, 94)( 70, 95)( 71, 96)( 72, 97)
( 73, 88)( 74, 89)( 75, 90)( 76, 91)( 77, 92)(128,133)(129,134)(130,135)
(131,136)(132,137)(138,148)(139,149)(140,150)(141,151)(142,152)(153,233)
(154,234)(155,235)(156,236)(157,237)(158,228)(159,229)(160,230)(161,231)
(162,232)(163,248)(164,249)(165,250)(166,251)(167,252)(168,243)(169,244)
(170,245)(171,246)(172,247)(173,238)(174,239)(175,240)(176,241)(177,242)
(178,208)(179,209)(180,210)(181,211)(182,212)(183,203)(184,204)(185,205)
(186,206)(187,207)(188,223)(189,224)(190,225)(191,226)(192,227)(193,218)
(194,219)(195,220)(196,221)(197,222)(198,213)(199,214)(200,215)(201,216)
(202,217);
s3 := Sym(252)!( 3,153)( 4,157)( 5,156)( 6,155)( 7,154)( 8,159)( 9,158)
( 10,162)( 11,161)( 12,160)( 13,165)( 14,164)( 15,163)( 16,167)( 17,166)
( 18,171)( 19,170)( 20,169)( 21,168)( 22,172)( 23,177)( 24,176)( 25,175)
( 26,174)( 27,173)( 28,128)( 29,132)( 30,131)( 31,130)( 32,129)( 33,134)
( 34,133)( 35,137)( 36,136)( 37,135)( 38,140)( 39,139)( 40,138)( 41,142)
( 42,141)( 43,146)( 44,145)( 45,144)( 46,143)( 47,147)( 48,152)( 49,151)
( 50,150)( 51,149)( 52,148)( 53,228)( 54,232)( 55,231)( 56,230)( 57,229)
( 58,234)( 59,233)( 60,237)( 61,236)( 62,235)( 63,240)( 64,239)( 65,238)
( 66,242)( 67,241)( 68,246)( 69,245)( 70,244)( 71,243)( 72,247)( 73,252)
( 74,251)( 75,250)( 76,249)( 77,248)( 78,203)( 79,207)( 80,206)( 81,205)
( 82,204)( 83,209)( 84,208)( 85,212)( 86,211)( 87,210)( 88,215)( 89,214)
( 90,213)( 91,217)( 92,216)( 93,221)( 94,220)( 95,219)( 96,218)( 97,222)
( 98,227)( 99,226)(100,225)(101,224)(102,223)(103,178)(104,182)(105,181)
(106,180)(107,179)(108,184)(109,183)(110,187)(111,186)(112,185)(113,190)
(114,189)(115,188)(116,192)(117,191)(118,196)(119,195)(120,194)(121,193)
(122,197)(123,202)(124,201)(125,200)(126,199)(127,198);
poly := sub<Sym(252)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2,
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 >;
to this polytope