Polytope of Type {2,4,10,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,10,10}*1600c
if this polytope has a name.
Group : SmallGroup(1600,10205)
Rank : 5
Schlafli Type : {2,4,10,10}
Number of vertices, edges, etc : 2, 4, 20, 50, 10
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 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 : {2,4,10,5}*800, {2,2,10,10}*800b
4-fold quotients : {2,2,10,5}*400
5-fold quotients : {2,4,2,10}*320
10-fold quotients : {2,4,2,5}*160, {2,2,2,10}*160
20-fold quotients : {2,2,2,5}*80
25-fold quotients : {2,4,2,2}*64
50-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 53)( 4, 54)( 5, 55)( 6, 56)( 7, 57)( 8, 58)( 9, 59)( 10, 60)
( 11, 61)( 12, 62)( 13, 63)( 14, 64)( 15, 65)( 16, 66)( 17, 67)( 18, 68)
( 19, 69)( 20, 70)( 21, 71)( 22, 72)( 23, 73)( 24, 74)( 25, 75)( 26, 76)
( 27, 77)( 28, 78)( 29, 79)( 30, 80)( 31, 81)( 32, 82)( 33, 83)( 34, 84)
( 35, 85)( 36, 86)( 37, 87)( 38, 88)( 39, 89)( 40, 90)( 41, 91)( 42, 92)
( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)( 48, 98)( 49, 99)( 50,100)
( 51,101)( 52,102)(103,153)(104,154)(105,155)(106,156)(107,157)(108,158)
(109,159)(110,160)(111,161)(112,162)(113,163)(114,164)(115,165)(116,166)
(117,167)(118,168)(119,169)(120,170)(121,171)(122,172)(123,173)(124,174)
(125,175)(126,176)(127,177)(128,178)(129,179)(130,180)(131,181)(132,182)
(133,183)(134,184)(135,185)(136,186)(137,187)(138,188)(139,189)(140,190)
(141,191)(142,192)(143,193)(144,194)(145,195)(146,196)(147,197)(148,198)
(149,199)(150,200)(151,201)(152,202);;
s2 := ( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 53, 78)( 54, 82)( 55, 81)( 56, 80)
( 57, 79)( 58, 83)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 88)( 64, 92)
( 65, 91)( 66, 90)( 67, 89)( 68, 93)( 69, 97)( 70, 96)( 71, 95)( 72, 94)
( 73, 98)( 74,102)( 75,101)( 76,100)( 77, 99)(104,107)(105,106)(109,112)
(110,111)(114,117)(115,116)(119,122)(120,121)(124,127)(125,126)(129,132)
(130,131)(134,137)(135,136)(139,142)(140,141)(144,147)(145,146)(149,152)
(150,151)(153,178)(154,182)(155,181)(156,180)(157,179)(158,183)(159,187)
(160,186)(161,185)(162,184)(163,188)(164,192)(165,191)(166,190)(167,189)
(168,193)(169,197)(170,196)(171,195)(172,194)(173,198)(174,202)(175,201)
(176,200)(177,199);;
s3 := ( 3, 4)( 5, 7)( 8, 24)( 9, 23)( 10, 27)( 11, 26)( 12, 25)( 13, 19)
( 14, 18)( 15, 22)( 16, 21)( 17, 20)( 28, 29)( 30, 32)( 33, 49)( 34, 48)
( 35, 52)( 36, 51)( 37, 50)( 38, 44)( 39, 43)( 40, 47)( 41, 46)( 42, 45)
( 53, 54)( 55, 57)( 58, 74)( 59, 73)( 60, 77)( 61, 76)( 62, 75)( 63, 69)
( 64, 68)( 65, 72)( 66, 71)( 67, 70)( 78, 79)( 80, 82)( 83, 99)( 84, 98)
( 85,102)( 86,101)( 87,100)( 88, 94)( 89, 93)( 90, 97)( 91, 96)( 92, 95)
(103,104)(105,107)(108,124)(109,123)(110,127)(111,126)(112,125)(113,119)
(114,118)(115,122)(116,121)(117,120)(128,129)(130,132)(133,149)(134,148)
(135,152)(136,151)(137,150)(138,144)(139,143)(140,147)(141,146)(142,145)
(153,154)(155,157)(158,174)(159,173)(160,177)(161,176)(162,175)(163,169)
(164,168)(165,172)(166,171)(167,170)(178,179)(180,182)(183,199)(184,198)
(185,202)(186,201)(187,200)(188,194)(189,193)(190,197)(191,196)(192,195);;
s4 := ( 3,108)( 4,112)( 5,111)( 6,110)( 7,109)( 8,103)( 9,107)( 10,106)
( 11,105)( 12,104)( 13,123)( 14,127)( 15,126)( 16,125)( 17,124)( 18,118)
( 19,122)( 20,121)( 21,120)( 22,119)( 23,113)( 24,117)( 25,116)( 26,115)
( 27,114)( 28,133)( 29,137)( 30,136)( 31,135)( 32,134)( 33,128)( 34,132)
( 35,131)( 36,130)( 37,129)( 38,148)( 39,152)( 40,151)( 41,150)( 42,149)
( 43,143)( 44,147)( 45,146)( 46,145)( 47,144)( 48,138)( 49,142)( 50,141)
( 51,140)( 52,139)( 53,158)( 54,162)( 55,161)( 56,160)( 57,159)( 58,153)
( 59,157)( 60,156)( 61,155)( 62,154)( 63,173)( 64,177)( 65,176)( 66,175)
( 67,174)( 68,168)( 69,172)( 70,171)( 71,170)( 72,169)( 73,163)( 74,167)
( 75,166)( 76,165)( 77,164)( 78,183)( 79,187)( 80,186)( 81,185)( 82,184)
( 83,178)( 84,182)( 85,181)( 86,180)( 87,179)( 88,198)( 89,202)( 90,201)
( 91,200)( 92,199)( 93,193)( 94,197)( 95,196)( 96,195)( 97,194)( 98,188)
( 99,192)(100,191)(101,190)(102,189);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(202)!(1,2);
s1 := Sym(202)!( 3, 53)( 4, 54)( 5, 55)( 6, 56)( 7, 57)( 8, 58)( 9, 59)
( 10, 60)( 11, 61)( 12, 62)( 13, 63)( 14, 64)( 15, 65)( 16, 66)( 17, 67)
( 18, 68)( 19, 69)( 20, 70)( 21, 71)( 22, 72)( 23, 73)( 24, 74)( 25, 75)
( 26, 76)( 27, 77)( 28, 78)( 29, 79)( 30, 80)( 31, 81)( 32, 82)( 33, 83)
( 34, 84)( 35, 85)( 36, 86)( 37, 87)( 38, 88)( 39, 89)( 40, 90)( 41, 91)
( 42, 92)( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)( 48, 98)( 49, 99)
( 50,100)( 51,101)( 52,102)(103,153)(104,154)(105,155)(106,156)(107,157)
(108,158)(109,159)(110,160)(111,161)(112,162)(113,163)(114,164)(115,165)
(116,166)(117,167)(118,168)(119,169)(120,170)(121,171)(122,172)(123,173)
(124,174)(125,175)(126,176)(127,177)(128,178)(129,179)(130,180)(131,181)
(132,182)(133,183)(134,184)(135,185)(136,186)(137,187)(138,188)(139,189)
(140,190)(141,191)(142,192)(143,193)(144,194)(145,195)(146,196)(147,197)
(148,198)(149,199)(150,200)(151,201)(152,202);
s2 := Sym(202)!( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)
( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 53, 78)( 54, 82)( 55, 81)
( 56, 80)( 57, 79)( 58, 83)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 88)
( 64, 92)( 65, 91)( 66, 90)( 67, 89)( 68, 93)( 69, 97)( 70, 96)( 71, 95)
( 72, 94)( 73, 98)( 74,102)( 75,101)( 76,100)( 77, 99)(104,107)(105,106)
(109,112)(110,111)(114,117)(115,116)(119,122)(120,121)(124,127)(125,126)
(129,132)(130,131)(134,137)(135,136)(139,142)(140,141)(144,147)(145,146)
(149,152)(150,151)(153,178)(154,182)(155,181)(156,180)(157,179)(158,183)
(159,187)(160,186)(161,185)(162,184)(163,188)(164,192)(165,191)(166,190)
(167,189)(168,193)(169,197)(170,196)(171,195)(172,194)(173,198)(174,202)
(175,201)(176,200)(177,199);
s3 := Sym(202)!( 3, 4)( 5, 7)( 8, 24)( 9, 23)( 10, 27)( 11, 26)( 12, 25)
( 13, 19)( 14, 18)( 15, 22)( 16, 21)( 17, 20)( 28, 29)( 30, 32)( 33, 49)
( 34, 48)( 35, 52)( 36, 51)( 37, 50)( 38, 44)( 39, 43)( 40, 47)( 41, 46)
( 42, 45)( 53, 54)( 55, 57)( 58, 74)( 59, 73)( 60, 77)( 61, 76)( 62, 75)
( 63, 69)( 64, 68)( 65, 72)( 66, 71)( 67, 70)( 78, 79)( 80, 82)( 83, 99)
( 84, 98)( 85,102)( 86,101)( 87,100)( 88, 94)( 89, 93)( 90, 97)( 91, 96)
( 92, 95)(103,104)(105,107)(108,124)(109,123)(110,127)(111,126)(112,125)
(113,119)(114,118)(115,122)(116,121)(117,120)(128,129)(130,132)(133,149)
(134,148)(135,152)(136,151)(137,150)(138,144)(139,143)(140,147)(141,146)
(142,145)(153,154)(155,157)(158,174)(159,173)(160,177)(161,176)(162,175)
(163,169)(164,168)(165,172)(166,171)(167,170)(178,179)(180,182)(183,199)
(184,198)(185,202)(186,201)(187,200)(188,194)(189,193)(190,197)(191,196)
(192,195);
s4 := Sym(202)!( 3,108)( 4,112)( 5,111)( 6,110)( 7,109)( 8,103)( 9,107)
( 10,106)( 11,105)( 12,104)( 13,123)( 14,127)( 15,126)( 16,125)( 17,124)
( 18,118)( 19,122)( 20,121)( 21,120)( 22,119)( 23,113)( 24,117)( 25,116)
( 26,115)( 27,114)( 28,133)( 29,137)( 30,136)( 31,135)( 32,134)( 33,128)
( 34,132)( 35,131)( 36,130)( 37,129)( 38,148)( 39,152)( 40,151)( 41,150)
( 42,149)( 43,143)( 44,147)( 45,146)( 46,145)( 47,144)( 48,138)( 49,142)
( 50,141)( 51,140)( 52,139)( 53,158)( 54,162)( 55,161)( 56,160)( 57,159)
( 58,153)( 59,157)( 60,156)( 61,155)( 62,154)( 63,173)( 64,177)( 65,176)
( 66,175)( 67,174)( 68,168)( 69,172)( 70,171)( 71,170)( 72,169)( 73,163)
( 74,167)( 75,166)( 76,165)( 77,164)( 78,183)( 79,187)( 80,186)( 81,185)
( 82,184)( 83,178)( 84,182)( 85,181)( 86,180)( 87,179)( 88,198)( 89,202)
( 90,201)( 91,200)( 92,199)( 93,193)( 94,197)( 95,196)( 96,195)( 97,194)
( 98,188)( 99,192)(100,191)(101,190)(102,189);
poly := sub<Sym(202)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope