Polytope of Type {4,8,6,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,6,2}*768b
if this polytope has a name.
Group : SmallGroup(768,1036167)
Rank : 5
Schlafli Type : {4,8,6,2}
Number of vertices, edges, etc : 4, 16, 24, 6, 2
Order of s0s1s2s3s4 : 24
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 : {4,4,6,2}*384
3-fold quotients : {4,8,2,2}*256b
4-fold quotients : {2,4,6,2}*192a, {4,2,6,2}*192
6-fold quotients : {4,4,2,2}*128
8-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96
12-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
16-fold quotients : {2,2,3,2}*48
24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 49)( 2, 50)( 3, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 64)( 14, 65)( 15, 66)( 16, 61)( 17, 62)( 18, 63)( 19, 70)( 20, 71)( 21, 72)( 22, 67)( 23, 68)( 24, 69)( 25, 73)( 26, 74)( 27, 75)( 28, 76)( 29, 77)( 30, 78)( 31, 79)( 32, 80)( 33, 81)( 34, 82)( 35, 83)( 36, 84)( 37, 88)( 38, 89)( 39, 90)( 40, 85)( 41, 86)( 42, 87)( 43, 94)( 44, 95)( 45, 96)( 46, 91)( 47, 92)( 48, 93)( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)(107,155)(108,156)(109,160)(110,161)(111,162)(112,157)(113,158)(114,159)(115,166)(116,167)(117,168)(118,163)(119,164)(120,165)(121,169)(122,170)(123,171)(124,172)(125,173)(126,174)(127,175)(128,176)(129,177)(130,178)(131,179)(132,180)(133,184)(134,185)(135,186)(136,181)(137,182)(138,183)(139,190)(140,191)(141,192)(142,187)(143,188)(144,189);;
s1 := ( 13, 16)( 14, 17)( 15, 18)( 19, 22)( 20, 23)( 21, 24)( 37, 40)( 38, 41)( 39, 42)( 43, 46)( 44, 47)( 45, 48)( 49, 55)( 50, 56)( 51, 57)( 52, 58)( 53, 59)( 54, 60)( 61, 70)( 62, 71)( 63, 72)( 64, 67)( 65, 68)( 66, 69)( 73, 79)( 74, 80)( 75, 81)( 76, 82)( 77, 83)( 78, 84)( 85, 94)( 86, 95)( 87, 96)( 88, 91)( 89, 92)( 90, 93)( 97,109)( 98,110)( 99,111)(100,112)(101,113)(102,114)(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)(121,133)(122,134)(123,135)(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)(131,143)(132,144)(145,166)(146,167)(147,168)(148,163)(149,164)(150,165)(151,160)(152,161)(153,162)(154,157)(155,158)(156,159)(169,190)(170,191)(171,192)(172,187)(173,188)(174,189)(175,184)(176,185)(177,186)(178,181)(179,182)(180,183);;
s2 := ( 1,121)( 2,123)( 3,122)( 4,124)( 5,126)( 6,125)( 7,130)( 8,132)( 9,131)( 10,127)( 11,129)( 12,128)( 13,136)( 14,138)( 15,137)( 16,133)( 17,135)( 18,134)( 19,139)( 20,141)( 21,140)( 22,142)( 23,144)( 24,143)( 25, 97)( 26, 99)( 27, 98)( 28,100)( 29,102)( 30,101)( 31,106)( 32,108)( 33,107)( 34,103)( 35,105)( 36,104)( 37,112)( 38,114)( 39,113)( 40,109)( 41,111)( 42,110)( 43,115)( 44,117)( 45,116)( 46,118)( 47,120)( 48,119)( 49,169)( 50,171)( 51,170)( 52,172)( 53,174)( 54,173)( 55,178)( 56,180)( 57,179)( 58,175)( 59,177)( 60,176)( 61,184)( 62,186)( 63,185)( 64,181)( 65,183)( 66,182)( 67,187)( 68,189)( 69,188)( 70,190)( 71,192)( 72,191)( 73,145)( 74,147)( 75,146)( 76,148)( 77,150)( 78,149)( 79,154)( 80,156)( 81,155)( 82,151)( 83,153)( 84,152)( 85,160)( 86,162)( 87,161)( 88,157)( 89,159)( 90,158)( 91,163)( 92,165)( 93,164)( 94,166)( 95,168)( 96,167);;
s3 := ( 1, 26)( 2, 25)( 3, 27)( 4, 29)( 5, 28)( 6, 30)( 7, 32)( 8, 31)( 9, 33)( 10, 35)( 11, 34)( 12, 36)( 13, 38)( 14, 37)( 15, 39)( 16, 41)( 17, 40)( 18, 42)( 19, 44)( 20, 43)( 21, 45)( 22, 47)( 23, 46)( 24, 48)( 49, 74)( 50, 73)( 51, 75)( 52, 77)( 53, 76)( 54, 78)( 55, 80)( 56, 79)( 57, 81)( 58, 83)( 59, 82)( 60, 84)( 61, 86)( 62, 85)( 63, 87)( 64, 89)( 65, 88)( 66, 90)( 67, 92)( 68, 91)( 69, 93)( 70, 95)( 71, 94)( 72, 96)( 97,122)( 98,121)( 99,123)(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)(107,130)(108,132)(109,134)(110,133)(111,135)(112,137)(113,136)(114,138)(115,140)(116,139)(117,141)(118,143)(119,142)(120,144)(145,170)(146,169)(147,171)(148,173)(149,172)(150,174)(151,176)(152,175)(153,177)(154,179)(155,178)(156,180)(157,182)(158,181)(159,183)(160,185)(161,184)(162,186)(163,188)(164,187)(165,189)(166,191)(167,190)(168,192);;
s4 := (193,194);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!( 1, 49)( 2, 50)( 3, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 64)( 14, 65)( 15, 66)( 16, 61)( 17, 62)( 18, 63)( 19, 70)( 20, 71)( 21, 72)( 22, 67)( 23, 68)( 24, 69)( 25, 73)( 26, 74)( 27, 75)( 28, 76)( 29, 77)( 30, 78)( 31, 79)( 32, 80)( 33, 81)( 34, 82)( 35, 83)( 36, 84)( 37, 88)( 38, 89)( 39, 90)( 40, 85)( 41, 86)( 42, 87)( 43, 94)( 44, 95)( 45, 96)( 46, 91)( 47, 92)( 48, 93)( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)(107,155)(108,156)(109,160)(110,161)(111,162)(112,157)(113,158)(114,159)(115,166)(116,167)(117,168)(118,163)(119,164)(120,165)(121,169)(122,170)(123,171)(124,172)(125,173)(126,174)(127,175)(128,176)(129,177)(130,178)(131,179)(132,180)(133,184)(134,185)(135,186)(136,181)(137,182)(138,183)(139,190)(140,191)(141,192)(142,187)(143,188)(144,189);
s1 := Sym(194)!( 13, 16)( 14, 17)( 15, 18)( 19, 22)( 20, 23)( 21, 24)( 37, 40)( 38, 41)( 39, 42)( 43, 46)( 44, 47)( 45, 48)( 49, 55)( 50, 56)( 51, 57)( 52, 58)( 53, 59)( 54, 60)( 61, 70)( 62, 71)( 63, 72)( 64, 67)( 65, 68)( 66, 69)( 73, 79)( 74, 80)( 75, 81)( 76, 82)( 77, 83)( 78, 84)( 85, 94)( 86, 95)( 87, 96)( 88, 91)( 89, 92)( 90, 93)( 97,109)( 98,110)( 99,111)(100,112)(101,113)(102,114)(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)(121,133)(122,134)(123,135)(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)(131,143)(132,144)(145,166)(146,167)(147,168)(148,163)(149,164)(150,165)(151,160)(152,161)(153,162)(154,157)(155,158)(156,159)(169,190)(170,191)(171,192)(172,187)(173,188)(174,189)(175,184)(176,185)(177,186)(178,181)(179,182)(180,183);
s2 := Sym(194)!( 1,121)( 2,123)( 3,122)( 4,124)( 5,126)( 6,125)( 7,130)( 8,132)( 9,131)( 10,127)( 11,129)( 12,128)( 13,136)( 14,138)( 15,137)( 16,133)( 17,135)( 18,134)( 19,139)( 20,141)( 21,140)( 22,142)( 23,144)( 24,143)( 25, 97)( 26, 99)( 27, 98)( 28,100)( 29,102)( 30,101)( 31,106)( 32,108)( 33,107)( 34,103)( 35,105)( 36,104)( 37,112)( 38,114)( 39,113)( 40,109)( 41,111)( 42,110)( 43,115)( 44,117)( 45,116)( 46,118)( 47,120)( 48,119)( 49,169)( 50,171)( 51,170)( 52,172)( 53,174)( 54,173)( 55,178)( 56,180)( 57,179)( 58,175)( 59,177)( 60,176)( 61,184)( 62,186)( 63,185)( 64,181)( 65,183)( 66,182)( 67,187)( 68,189)( 69,188)( 70,190)( 71,192)( 72,191)( 73,145)( 74,147)( 75,146)( 76,148)( 77,150)( 78,149)( 79,154)( 80,156)( 81,155)( 82,151)( 83,153)( 84,152)( 85,160)( 86,162)( 87,161)( 88,157)( 89,159)( 90,158)( 91,163)( 92,165)( 93,164)( 94,166)( 95,168)( 96,167);
s3 := Sym(194)!( 1, 26)( 2, 25)( 3, 27)( 4, 29)( 5, 28)( 6, 30)( 7, 32)( 8, 31)( 9, 33)( 10, 35)( 11, 34)( 12, 36)( 13, 38)( 14, 37)( 15, 39)( 16, 41)( 17, 40)( 18, 42)( 19, 44)( 20, 43)( 21, 45)( 22, 47)( 23, 46)( 24, 48)( 49, 74)( 50, 73)( 51, 75)( 52, 77)( 53, 76)( 54, 78)( 55, 80)( 56, 79)( 57, 81)( 58, 83)( 59, 82)( 60, 84)( 61, 86)( 62, 85)( 63, 87)( 64, 89)( 65, 88)( 66, 90)( 67, 92)( 68, 91)( 69, 93)( 70, 95)( 71, 94)( 72, 96)( 97,122)( 98,121)( 99,123)(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)(107,130)(108,132)(109,134)(110,133)(111,135)(112,137)(113,136)(114,138)(115,140)(116,139)(117,141)(118,143)(119,142)(120,144)(145,170)(146,169)(147,171)(148,173)(149,172)(150,174)(151,176)(152,175)(153,177)(154,179)(155,178)(156,180)(157,182)(158,181)(159,183)(160,185)(161,184)(162,186)(163,188)(164,187)(165,189)(166,191)(167,190)(168,192);
s4 := Sym(194)!(193,194);
poly := sub<Sym(194)|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*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope