Polytope of Type {2,8,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,4,6}*768a
if this polytope has a name.
Group : SmallGroup(768,1035859)
Rank : 5
Schlafli Type : {2,8,4,6}
Number of vertices, edges, etc : 2, 8, 16, 12, 6
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 : {2,4,4,6}*384, {2,8,2,6}*384
3-fold quotients : {2,8,4,2}*256a
4-fold quotients : {2,8,2,3}*192, {2,2,4,6}*192a, {2,4,2,6}*192
6-fold quotients : {2,4,4,2}*128, {2,8,2,2}*128
8-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96
12-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
16-fold quotients : {2,2,2,3}*48
24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,105)( 10,106)
( 11,107)( 12,108)( 13,109)( 14,110)( 15,114)( 16,115)( 17,116)( 18,111)
( 19,112)( 20,113)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)( 26,119)
( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)( 33,129)( 34,130)
( 35,131)( 36,132)( 37,133)( 38,134)( 39,138)( 40,139)( 41,140)( 42,135)
( 43,136)( 44,137)( 45,144)( 46,145)( 47,146)( 48,141)( 49,142)( 50,143)
( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,153)( 58,154)
( 59,155)( 60,156)( 61,157)( 62,158)( 63,162)( 64,163)( 65,164)( 66,159)
( 67,160)( 68,161)( 69,168)( 70,169)( 71,170)( 72,165)( 73,166)( 74,167)
( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)( 80,176)( 81,177)( 82,178)
( 83,179)( 84,180)( 85,181)( 86,182)( 87,186)( 88,187)( 89,188)( 90,183)
( 91,184)( 92,185)( 93,192)( 94,193)( 95,194)( 96,189)( 97,190)( 98,191);;
s2 := ( 15, 18)( 16, 19)( 17, 20)( 21, 24)( 22, 25)( 23, 26)( 39, 42)( 40, 43)
( 41, 44)( 45, 48)( 46, 49)( 47, 50)( 51, 57)( 52, 58)( 53, 59)( 54, 60)
( 55, 61)( 56, 62)( 63, 72)( 64, 73)( 65, 74)( 66, 69)( 67, 70)( 68, 71)
( 75, 81)( 76, 82)( 77, 83)( 78, 84)( 79, 85)( 80, 86)( 87, 96)( 88, 97)
( 89, 98)( 90, 93)( 91, 94)( 92, 95)( 99,111)(100,112)(101,113)(102,114)
(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)(109,121)(110,122)
(123,135)(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)
(131,143)(132,144)(133,145)(134,146)(147,165)(148,166)(149,167)(150,168)
(151,169)(152,170)(153,159)(154,160)(155,161)(156,162)(157,163)(158,164)
(171,189)(172,190)(173,191)(174,192)(175,193)(176,194)(177,183)(178,184)
(179,185)(180,186)(181,187)(182,188);;
s3 := ( 3, 75)( 4, 77)( 5, 76)( 6, 78)( 7, 80)( 8, 79)( 9, 81)( 10, 83)
( 11, 82)( 12, 84)( 13, 86)( 14, 85)( 15, 87)( 16, 89)( 17, 88)( 18, 90)
( 19, 92)( 20, 91)( 21, 93)( 22, 95)( 23, 94)( 24, 96)( 25, 98)( 26, 97)
( 27, 51)( 28, 53)( 29, 52)( 30, 54)( 31, 56)( 32, 55)( 33, 57)( 34, 59)
( 35, 58)( 36, 60)( 37, 62)( 38, 61)( 39, 63)( 40, 65)( 41, 64)( 42, 66)
( 43, 68)( 44, 67)( 45, 69)( 46, 71)( 47, 70)( 48, 72)( 49, 74)( 50, 73)
( 99,171)(100,173)(101,172)(102,174)(103,176)(104,175)(105,177)(106,179)
(107,178)(108,180)(109,182)(110,181)(111,183)(112,185)(113,184)(114,186)
(115,188)(116,187)(117,189)(118,191)(119,190)(120,192)(121,194)(122,193)
(123,147)(124,149)(125,148)(126,150)(127,152)(128,151)(129,153)(130,155)
(131,154)(132,156)(133,158)(134,157)(135,159)(136,161)(137,160)(138,162)
(139,164)(140,163)(141,165)(142,167)(143,166)(144,168)(145,170)(146,169);;
s4 := ( 3, 28)( 4, 27)( 5, 29)( 6, 31)( 7, 30)( 8, 32)( 9, 34)( 10, 33)
( 11, 35)( 12, 37)( 13, 36)( 14, 38)( 15, 40)( 16, 39)( 17, 41)( 18, 43)
( 19, 42)( 20, 44)( 21, 46)( 22, 45)( 23, 47)( 24, 49)( 25, 48)( 26, 50)
( 51, 76)( 52, 75)( 53, 77)( 54, 79)( 55, 78)( 56, 80)( 57, 82)( 58, 81)
( 59, 83)( 60, 85)( 61, 84)( 62, 86)( 63, 88)( 64, 87)( 65, 89)( 66, 91)
( 67, 90)( 68, 92)( 69, 94)( 70, 93)( 71, 95)( 72, 97)( 73, 96)( 74, 98)
( 99,124)(100,123)(101,125)(102,127)(103,126)(104,128)(105,130)(106,129)
(107,131)(108,133)(109,132)(110,134)(111,136)(112,135)(113,137)(114,139)
(115,138)(116,140)(117,142)(118,141)(119,143)(120,145)(121,144)(122,146)
(147,172)(148,171)(149,173)(150,175)(151,174)(152,176)(153,178)(154,177)
(155,179)(156,181)(157,180)(158,182)(159,184)(160,183)(161,185)(162,187)
(163,186)(164,188)(165,190)(166,189)(167,191)(168,193)(169,192)(170,194);;
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*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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,105)
( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,114)( 16,115)( 17,116)
( 18,111)( 19,112)( 20,113)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)
( 26,119)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)( 33,129)
( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,138)( 40,139)( 41,140)
( 42,135)( 43,136)( 44,137)( 45,144)( 46,145)( 47,146)( 48,141)( 49,142)
( 50,143)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,153)
( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,162)( 64,163)( 65,164)
( 66,159)( 67,160)( 68,161)( 69,168)( 70,169)( 71,170)( 72,165)( 73,166)
( 74,167)( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)( 80,176)( 81,177)
( 82,178)( 83,179)( 84,180)( 85,181)( 86,182)( 87,186)( 88,187)( 89,188)
( 90,183)( 91,184)( 92,185)( 93,192)( 94,193)( 95,194)( 96,189)( 97,190)
( 98,191);
s2 := Sym(194)!( 15, 18)( 16, 19)( 17, 20)( 21, 24)( 22, 25)( 23, 26)( 39, 42)
( 40, 43)( 41, 44)( 45, 48)( 46, 49)( 47, 50)( 51, 57)( 52, 58)( 53, 59)
( 54, 60)( 55, 61)( 56, 62)( 63, 72)( 64, 73)( 65, 74)( 66, 69)( 67, 70)
( 68, 71)( 75, 81)( 76, 82)( 77, 83)( 78, 84)( 79, 85)( 80, 86)( 87, 96)
( 88, 97)( 89, 98)( 90, 93)( 91, 94)( 92, 95)( 99,111)(100,112)(101,113)
(102,114)(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)(109,121)
(110,122)(123,135)(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)
(130,142)(131,143)(132,144)(133,145)(134,146)(147,165)(148,166)(149,167)
(150,168)(151,169)(152,170)(153,159)(154,160)(155,161)(156,162)(157,163)
(158,164)(171,189)(172,190)(173,191)(174,192)(175,193)(176,194)(177,183)
(178,184)(179,185)(180,186)(181,187)(182,188);
s3 := Sym(194)!( 3, 75)( 4, 77)( 5, 76)( 6, 78)( 7, 80)( 8, 79)( 9, 81)
( 10, 83)( 11, 82)( 12, 84)( 13, 86)( 14, 85)( 15, 87)( 16, 89)( 17, 88)
( 18, 90)( 19, 92)( 20, 91)( 21, 93)( 22, 95)( 23, 94)( 24, 96)( 25, 98)
( 26, 97)( 27, 51)( 28, 53)( 29, 52)( 30, 54)( 31, 56)( 32, 55)( 33, 57)
( 34, 59)( 35, 58)( 36, 60)( 37, 62)( 38, 61)( 39, 63)( 40, 65)( 41, 64)
( 42, 66)( 43, 68)( 44, 67)( 45, 69)( 46, 71)( 47, 70)( 48, 72)( 49, 74)
( 50, 73)( 99,171)(100,173)(101,172)(102,174)(103,176)(104,175)(105,177)
(106,179)(107,178)(108,180)(109,182)(110,181)(111,183)(112,185)(113,184)
(114,186)(115,188)(116,187)(117,189)(118,191)(119,190)(120,192)(121,194)
(122,193)(123,147)(124,149)(125,148)(126,150)(127,152)(128,151)(129,153)
(130,155)(131,154)(132,156)(133,158)(134,157)(135,159)(136,161)(137,160)
(138,162)(139,164)(140,163)(141,165)(142,167)(143,166)(144,168)(145,170)
(146,169);
s4 := Sym(194)!( 3, 28)( 4, 27)( 5, 29)( 6, 31)( 7, 30)( 8, 32)( 9, 34)
( 10, 33)( 11, 35)( 12, 37)( 13, 36)( 14, 38)( 15, 40)( 16, 39)( 17, 41)
( 18, 43)( 19, 42)( 20, 44)( 21, 46)( 22, 45)( 23, 47)( 24, 49)( 25, 48)
( 26, 50)( 51, 76)( 52, 75)( 53, 77)( 54, 79)( 55, 78)( 56, 80)( 57, 82)
( 58, 81)( 59, 83)( 60, 85)( 61, 84)( 62, 86)( 63, 88)( 64, 87)( 65, 89)
( 66, 91)( 67, 90)( 68, 92)( 69, 94)( 70, 93)( 71, 95)( 72, 97)( 73, 96)
( 74, 98)( 99,124)(100,123)(101,125)(102,127)(103,126)(104,128)(105,130)
(106,129)(107,131)(108,133)(109,132)(110,134)(111,136)(112,135)(113,137)
(114,139)(115,138)(116,140)(117,142)(118,141)(119,143)(120,145)(121,144)
(122,146)(147,172)(148,171)(149,173)(150,175)(151,174)(152,176)(153,178)
(154,177)(155,179)(156,181)(157,180)(158,182)(159,184)(160,183)(161,185)
(162,187)(163,186)(164,188)(165,190)(166,189)(167,191)(168,193)(169,192)
(170,194);
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*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*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope