Polytope of Type {10,8,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8,10}*1600
Also Known As : {{10,8|2},{8,10|2}}. if this polytope has another name.
Group : SmallGroup(1600,8167)
Rank : 4
Schlafli Type : {10,8,10}
Number of vertices, edges, etc : 10, 40, 40, 10
Order of s₀s₁s₂s₃ : 40
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) :
   2-fold quotients : {10,4,10}*800
   4-fold quotients : {10,2,10}*400
   5-fold quotients : {2,8,10}*320, {10,8,2}*320
   8-fold quotients : {5,2,10}*200, {10,2,5}*200
   10-fold quotients : {2,4,10}*160, {10,4,2}*160
   16-fold quotients : {5,2,5}*100
   20-fold quotients : {2,2,10}*80, {10,2,2}*80
   25-fold quotients : {2,8,2}*64
   40-fold quotients : {2,2,5}*40, {5,2,2}*40
   50-fold quotients : {2,4,2}*32
   100-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);;
s1 := (  1,  6)(  2,  7)(  3,  8)(  4,  9)(  5, 10)( 11, 21)( 12, 22)( 13, 23)
( 14, 24)( 15, 25)( 26, 31)( 27, 32)( 28, 33)( 29, 34)( 30, 35)( 36, 46)
( 37, 47)( 38, 48)( 39, 49)( 40, 50)( 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)(101,156)(102,157)(103,158)
(104,159)(105,160)(106,151)(107,152)(108,153)(109,154)(110,155)(111,171)
(112,172)(113,173)(114,174)(115,175)(116,166)(117,167)(118,168)(119,169)
(120,170)(121,161)(122,162)(123,163)(124,164)(125,165)(126,181)(127,182)
(128,183)(129,184)(130,185)(131,176)(132,177)(133,178)(134,179)(135,180)
(136,196)(137,197)(138,198)(139,199)(140,200)(141,191)(142,192)(143,193)
(144,194)(145,195)(146,186)(147,187)(148,188)(149,189)(150,190);;
s2 := (  1,101)(  2,105)(  3,104)(  4,103)(  5,102)(  6,106)(  7,110)(  8,109)
(  9,108)( 10,107)( 11,111)( 12,115)( 13,114)( 14,113)( 15,112)( 16,116)
( 17,120)( 18,119)( 19,118)( 20,117)( 21,121)( 22,125)( 23,124)( 24,123)
( 25,122)( 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)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)( 56,181)
( 57,185)( 58,184)( 59,183)( 60,182)( 61,186)( 62,190)( 63,189)( 64,188)
( 65,187)( 66,191)( 67,195)( 68,194)( 69,193)( 70,192)( 71,196)( 72,200)
( 73,199)( 74,198)( 75,197)( 76,151)( 77,155)( 78,154)( 79,153)( 80,152)
( 81,156)( 82,160)( 83,159)( 84,158)( 85,157)( 86,161)( 87,165)( 88,164)
( 89,163)( 90,162)( 91,166)( 92,170)( 93,169)( 94,168)( 95,167)( 96,171)
( 97,175)( 98,174)( 99,173)(100,172);;
s3 := (  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)
( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)
( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)
( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)( 78, 80)
( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)
(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)(118,120)
(121,122)(123,125)(126,127)(128,130)(131,132)(133,135)(136,137)(138,140)
(141,142)(143,145)(146,147)(148,150)(151,152)(153,155)(156,157)(158,160)
(161,162)(163,165)(166,167)(168,170)(171,172)(173,175)(176,177)(178,180)
(181,182)(183,185)(186,187)(188,190)(191,192)(193,195)(196,197)(198,200);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(200)!(  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);
s1 := Sym(200)!(  1,  6)(  2,  7)(  3,  8)(  4,  9)(  5, 10)( 11, 21)( 12, 22)
( 13, 23)( 14, 24)( 15, 25)( 26, 31)( 27, 32)( 28, 33)( 29, 34)( 30, 35)
( 36, 46)( 37, 47)( 38, 48)( 39, 49)( 40, 50)( 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)(101,156)(102,157)
(103,158)(104,159)(105,160)(106,151)(107,152)(108,153)(109,154)(110,155)
(111,171)(112,172)(113,173)(114,174)(115,175)(116,166)(117,167)(118,168)
(119,169)(120,170)(121,161)(122,162)(123,163)(124,164)(125,165)(126,181)
(127,182)(128,183)(129,184)(130,185)(131,176)(132,177)(133,178)(134,179)
(135,180)(136,196)(137,197)(138,198)(139,199)(140,200)(141,191)(142,192)
(143,193)(144,194)(145,195)(146,186)(147,187)(148,188)(149,189)(150,190);
s2 := Sym(200)!(  1,101)(  2,105)(  3,104)(  4,103)(  5,102)(  6,106)(  7,110)
(  8,109)(  9,108)( 10,107)( 11,111)( 12,115)( 13,114)( 14,113)( 15,112)
( 16,116)( 17,120)( 18,119)( 19,118)( 20,117)( 21,121)( 22,125)( 23,124)
( 24,123)( 25,122)( 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)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)
( 56,181)( 57,185)( 58,184)( 59,183)( 60,182)( 61,186)( 62,190)( 63,189)
( 64,188)( 65,187)( 66,191)( 67,195)( 68,194)( 69,193)( 70,192)( 71,196)
( 72,200)( 73,199)( 74,198)( 75,197)( 76,151)( 77,155)( 78,154)( 79,153)
( 80,152)( 81,156)( 82,160)( 83,159)( 84,158)( 85,157)( 86,161)( 87,165)
( 88,164)( 89,163)( 90,162)( 91,166)( 92,170)( 93,169)( 94,168)( 95,167)
( 96,171)( 97,175)( 98,174)( 99,173)(100,172);
s3 := Sym(200)!(  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)
( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)
( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)
( 58, 60)( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)
( 78, 80)( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)
( 98,100)(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)
(118,120)(121,122)(123,125)(126,127)(128,130)(131,132)(133,135)(136,137)
(138,140)(141,142)(143,145)(146,147)(148,150)(151,152)(153,155)(156,157)
(158,160)(161,162)(163,165)(166,167)(168,170)(171,172)(173,175)(176,177)
(178,180)(181,182)(183,185)(186,187)(188,190)(191,192)(193,195)(196,197)
(198,200);
poly := sub<Sym(200)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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