Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,4,8}

Atlas Canonical Name {10,4,8}*1600

Overview

Group
SmallGroup(1600,6672)
Rank
4
Schläfli Type
{10,4,8}
Vertices, edges, …
25, 50, 40, 8
Order of s0s1s2s3
8
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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,  6)(  2, 17)(  4, 14)(  5, 25)(  7, 12)(  8, 23)( 10, 20)( 11, 21)( 13, 18)( 19, 24)( 26, 31)( 27, 42)( 29, 39)( 30, 50)( 32, 37)( 33, 48)( 35, 45)( 36, 46)( 38, 43)( 44, 49)( 51, 56)( 52, 67)( 54, 64)( 55, 75)( 57, 62)( 58, 73)( 60, 70)( 61, 71)( 63, 68)( 69, 74)( 76, 81)( 77, 92)( 79, 89)( 80,100)( 82, 87)( 83, 98)( 85, 95)( 86, 96)( 88, 93)( 94, 99)(101,106)(102,117)(104,114)(105,125)(107,112)(108,123)(110,120)(111,121)(113,118)(119,124)(126,131)(127,142)(129,139)(130,150)(132,137)(133,148)(135,145)(136,146)(138,143)(144,149)(151,156)(152,167)(154,164)(155,175)(157,162)(158,173)(160,170)(161,171)(163,168)(169,174)(176,181)(177,192)(179,189)(180,200)(182,187)(183,198)(185,195)(186,196)(188,193)(194,199);;
s2 := (  2,  9)(  3, 12)(  4, 20)(  5, 23)(  6, 13)(  7, 16)(  8, 24)( 11, 25)( 15, 17)( 19, 21)( 27, 34)( 28, 37)( 29, 45)( 30, 48)( 31, 38)( 32, 41)( 33, 49)( 36, 50)( 40, 42)( 44, 46)( 51, 76)( 52, 84)( 53, 87)( 54, 95)( 55, 98)( 56, 88)( 57, 91)( 58, 99)( 59, 77)( 60, 85)( 61,100)( 62, 78)( 63, 81)( 64, 89)( 65, 92)( 66, 82)( 67, 90)( 68, 93)( 69, 96)( 70, 79)( 71, 94)( 72, 97)( 73, 80)( 74, 83)( 75, 86)(101,151)(102,159)(103,162)(104,170)(105,173)(106,163)(107,166)(108,174)(109,152)(110,160)(111,175)(112,153)(113,156)(114,164)(115,167)(116,157)(117,165)(118,168)(119,171)(120,154)(121,169)(122,172)(123,155)(124,158)(125,161)(126,176)(127,184)(128,187)(129,195)(130,198)(131,188)(132,191)(133,199)(134,177)(135,185)(136,200)(137,178)(138,181)(139,189)(140,192)(141,182)(142,190)(143,193)(144,196)(145,179)(146,194)(147,197)(148,180)(149,183)(150,186);;
s3 := (  1,101)(  2,102)(  3,103)(  4,104)(  5,105)(  6,106)(  7,107)(  8,108)(  9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)( 25,125)( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)( 32,132)( 33,133)( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)( 40,140)( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)( 48,148)( 49,149)( 50,150)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)( 56,181)( 57,182)( 58,183)( 59,184)( 60,185)( 61,186)( 62,187)( 63,188)( 64,189)( 65,190)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,196)( 72,197)( 73,198)( 74,199)( 75,200)( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)( 81,156)( 82,157)( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)( 89,164)( 90,165)( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)( 97,172)( 98,173)( 99,174)(100,175);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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,  6)(  2, 17)(  4, 14)(  5, 25)(  7, 12)(  8, 23)( 10, 20)( 11, 21)( 13, 18)( 19, 24)( 26, 31)( 27, 42)( 29, 39)( 30, 50)( 32, 37)( 33, 48)( 35, 45)( 36, 46)( 38, 43)( 44, 49)( 51, 56)( 52, 67)( 54, 64)( 55, 75)( 57, 62)( 58, 73)( 60, 70)( 61, 71)( 63, 68)( 69, 74)( 76, 81)( 77, 92)( 79, 89)( 80,100)( 82, 87)( 83, 98)( 85, 95)( 86, 96)( 88, 93)( 94, 99)(101,106)(102,117)(104,114)(105,125)(107,112)(108,123)(110,120)(111,121)(113,118)(119,124)(126,131)(127,142)(129,139)(130,150)(132,137)(133,148)(135,145)(136,146)(138,143)(144,149)(151,156)(152,167)(154,164)(155,175)(157,162)(158,173)(160,170)(161,171)(163,168)(169,174)(176,181)(177,192)(179,189)(180,200)(182,187)(183,198)(185,195)(186,196)(188,193)(194,199);
s2 := Sym(200)!(  2,  9)(  3, 12)(  4, 20)(  5, 23)(  6, 13)(  7, 16)(  8, 24)( 11, 25)( 15, 17)( 19, 21)( 27, 34)( 28, 37)( 29, 45)( 30, 48)( 31, 38)( 32, 41)( 33, 49)( 36, 50)( 40, 42)( 44, 46)( 51, 76)( 52, 84)( 53, 87)( 54, 95)( 55, 98)( 56, 88)( 57, 91)( 58, 99)( 59, 77)( 60, 85)( 61,100)( 62, 78)( 63, 81)( 64, 89)( 65, 92)( 66, 82)( 67, 90)( 68, 93)( 69, 96)( 70, 79)( 71, 94)( 72, 97)( 73, 80)( 74, 83)( 75, 86)(101,151)(102,159)(103,162)(104,170)(105,173)(106,163)(107,166)(108,174)(109,152)(110,160)(111,175)(112,153)(113,156)(114,164)(115,167)(116,157)(117,165)(118,168)(119,171)(120,154)(121,169)(122,172)(123,155)(124,158)(125,161)(126,176)(127,184)(128,187)(129,195)(130,198)(131,188)(132,191)(133,199)(134,177)(135,185)(136,200)(137,178)(138,181)(139,189)(140,192)(141,182)(142,190)(143,193)(144,196)(145,179)(146,194)(147,197)(148,180)(149,183)(150,186);
s3 := Sym(200)!(  1,101)(  2,102)(  3,103)(  4,104)(  5,105)(  6,106)(  7,107)(  8,108)(  9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)( 25,125)( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)( 32,132)( 33,133)( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)( 40,140)( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)( 48,148)( 49,149)( 50,150)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)( 56,181)( 57,182)( 58,183)( 59,184)( 60,185)( 61,186)( 62,187)( 63,188)( 64,189)( 65,190)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,196)( 72,197)( 73,198)( 74,199)( 75,200)( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)( 81,156)( 82,157)( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)( 89,164)( 90,165)( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)( 97,172)( 98,173)( 99,174)(100,175);
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.