Polytope of Type {10,40}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,40}*800c
if this polytope has a name.
Group : SmallGroup(800,703)
Rank : 3
Schlafli Type : {10,40}
Number of vertices, edges, etc : 10, 200, 40
Order of s0s1s2 : 40
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,40,2} of size 1600
Vertex Figure Of :
   {2,10,40} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,20}*400c
   4-fold quotients : {10,10}*200c
   5-fold quotients : {10,8}*160
   8-fold quotients : {5,10}*100
   10-fold quotients : {10,4}*80
   20-fold quotients : {10,2}*40
   25-fold quotients : {2,8}*32
   40-fold quotients : {5,2}*20
   50-fold quotients : {2,4}*16
   100-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,40}*1600b, {10,80}*1600c
Irregular Quotients (of which this is a minimal cover):
   None.

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);;
s1 := (  1,107)(  2,106)(  3,110)(  4,109)(  5,108)(  6,102)(  7,101)(  8,105)(  9,104)( 10,103)( 11,122)( 12,121)( 13,125)( 14,124)( 15,123)( 16,117)( 17,116)( 18,120)( 19,119)( 20,118)( 21,112)( 22,111)( 23,115)( 24,114)( 25,113)( 26,132)( 27,131)( 28,135)( 29,134)( 30,133)( 31,127)( 32,126)( 33,130)( 34,129)( 35,128)( 36,147)( 37,146)( 38,150)( 39,149)( 40,148)( 41,142)( 42,141)( 43,145)( 44,144)( 45,143)( 46,137)( 47,136)( 48,140)( 49,139)( 50,138)( 51,182)( 52,181)( 53,185)( 54,184)( 55,183)( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,197)( 62,196)( 63,200)( 64,199)( 65,198)( 66,192)( 67,191)( 68,195)( 69,194)( 70,193)( 71,187)( 72,186)( 73,190)( 74,189)( 75,188)( 76,157)( 77,156)( 78,160)( 79,159)( 80,158)( 81,152)( 82,151)( 83,155)( 84,154)( 85,153)( 86,172)( 87,171)( 88,175)( 89,174)( 90,173)( 91,167)( 92,166)( 93,170)( 94,169)( 95,168)( 96,162)( 97,161)( 98,165)( 99,164)(100,163);;
s2 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)( 63, 89)( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)(101,151)(102,155)(103,154)(104,153)(105,152)(106,156)(107,160)(108,159)(109,158)(110,157)(111,161)(112,165)(113,164)(114,163)(115,162)(116,166)(117,170)(118,169)(119,168)(120,167)(121,171)(122,175)(123,174)(124,173)(125,172)(126,176)(127,180)(128,179)(129,178)(130,177)(131,181)(132,185)(133,184)(134,183)(135,182)(136,186)(137,190)(138,189)(139,188)(140,187)(141,191)(142,195)(143,194)(144,193)(145,192)(146,196)(147,200)(148,199)(149,198)(150,197);;
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*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(200)!(  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);
s1 := Sym(200)!(  1,107)(  2,106)(  3,110)(  4,109)(  5,108)(  6,102)(  7,101)(  8,105)(  9,104)( 10,103)( 11,122)( 12,121)( 13,125)( 14,124)( 15,123)( 16,117)( 17,116)( 18,120)( 19,119)( 20,118)( 21,112)( 22,111)( 23,115)( 24,114)( 25,113)( 26,132)( 27,131)( 28,135)( 29,134)( 30,133)( 31,127)( 32,126)( 33,130)( 34,129)( 35,128)( 36,147)( 37,146)( 38,150)( 39,149)( 40,148)( 41,142)( 42,141)( 43,145)( 44,144)( 45,143)( 46,137)( 47,136)( 48,140)( 49,139)( 50,138)( 51,182)( 52,181)( 53,185)( 54,184)( 55,183)( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,197)( 62,196)( 63,200)( 64,199)( 65,198)( 66,192)( 67,191)( 68,195)( 69,194)( 70,193)( 71,187)( 72,186)( 73,190)( 74,189)( 75,188)( 76,157)( 77,156)( 78,160)( 79,159)( 80,158)( 81,152)( 82,151)( 83,155)( 84,154)( 85,153)( 86,172)( 87,171)( 88,175)( 89,174)( 90,173)( 91,167)( 92,166)( 93,170)( 94,169)( 95,168)( 96,162)( 97,161)( 98,165)( 99,164)(100,163);
s2 := Sym(200)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)( 63, 89)( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)(101,151)(102,155)(103,154)(104,153)(105,152)(106,156)(107,160)(108,159)(109,158)(110,157)(111,161)(112,165)(113,164)(114,163)(115,162)(116,166)(117,170)(118,169)(119,168)(120,167)(121,171)(122,175)(123,174)(124,173)(125,172)(126,176)(127,180)(128,179)(129,178)(130,177)(131,181)(132,185)(133,184)(134,183)(135,182)(136,186)(137,190)(138,189)(139,188)(140,187)(141,191)(142,195)(143,194)(144,193)(145,192)(146,196)(147,200)(148,199)(149,198)(150,197);
poly := sub<Sym(200)|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*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
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