Polytope of Type {2,4,8,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,8,6}*768b
if this polytope has a name.
Group : SmallGroup(768,1036167)
Rank : 5
Schlafli Type : {2,4,8,6}
Number of vertices, edges, etc : 2, 4, 16, 24, 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
3-fold quotients : {2,4,8,2}*256b
4-fold quotients : {2,2,4,6}*192a, {2,4,2,6}*192
6-fold quotients : {2,4,4,2}*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, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)( 10, 58)
( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 66)( 16, 67)( 17, 68)( 18, 63)
( 19, 64)( 20, 65)( 21, 72)( 22, 73)( 23, 74)( 24, 69)( 25, 70)( 26, 71)
( 27, 75)( 28, 76)( 29, 77)( 30, 78)( 31, 79)( 32, 80)( 33, 81)( 34, 82)
( 35, 83)( 36, 84)( 37, 85)( 38, 86)( 39, 90)( 40, 91)( 41, 92)( 42, 87)
( 43, 88)( 44, 89)( 45, 96)( 46, 97)( 47, 98)( 48, 93)( 49, 94)( 50, 95)
( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)
(107,155)(108,156)(109,157)(110,158)(111,162)(112,163)(113,164)(114,159)
(115,160)(116,161)(117,168)(118,169)(119,170)(120,165)(121,166)(122,167)
(123,171)(124,172)(125,173)(126,174)(127,175)(128,176)(129,177)(130,178)
(131,179)(132,180)(133,181)(134,182)(135,186)(136,187)(137,188)(138,183)
(139,184)(140,185)(141,192)(142,193)(143,194)(144,189)(145,190)(146,191);;
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)(147,168)(148,169)(149,170)(150,165)
(151,166)(152,167)(153,162)(154,163)(155,164)(156,159)(157,160)(158,161)
(171,192)(172,193)(173,194)(174,189)(175,190)(176,191)(177,186)(178,187)
(179,188)(180,183)(181,184)(182,185);;
s3 := ( 3,123)( 4,125)( 5,124)( 6,126)( 7,128)( 8,127)( 9,132)( 10,134)
( 11,133)( 12,129)( 13,131)( 14,130)( 15,138)( 16,140)( 17,139)( 18,135)
( 19,137)( 20,136)( 21,141)( 22,143)( 23,142)( 24,144)( 25,146)( 26,145)
( 27, 99)( 28,101)( 29,100)( 30,102)( 31,104)( 32,103)( 33,108)( 34,110)
( 35,109)( 36,105)( 37,107)( 38,106)( 39,114)( 40,116)( 41,115)( 42,111)
( 43,113)( 44,112)( 45,117)( 46,119)( 47,118)( 48,120)( 49,122)( 50,121)
( 51,171)( 52,173)( 53,172)( 54,174)( 55,176)( 56,175)( 57,180)( 58,182)
( 59,181)( 60,177)( 61,179)( 62,178)( 63,186)( 64,188)( 65,187)( 66,183)
( 67,185)( 68,184)( 69,189)( 70,191)( 71,190)( 72,192)( 73,194)( 74,193)
( 75,147)( 76,149)( 77,148)( 78,150)( 79,152)( 80,151)( 81,156)( 82,158)
( 83,157)( 84,153)( 85,155)( 86,154)( 87,162)( 88,164)( 89,163)( 90,159)
( 91,161)( 92,160)( 93,165)( 94,167)( 95,166)( 96,168)( 97,170)( 98,169);;
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*s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!( 3, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)
( 10, 58)( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 66)( 16, 67)( 17, 68)
( 18, 63)( 19, 64)( 20, 65)( 21, 72)( 22, 73)( 23, 74)( 24, 69)( 25, 70)
( 26, 71)( 27, 75)( 28, 76)( 29, 77)( 30, 78)( 31, 79)( 32, 80)( 33, 81)
( 34, 82)( 35, 83)( 36, 84)( 37, 85)( 38, 86)( 39, 90)( 40, 91)( 41, 92)
( 42, 87)( 43, 88)( 44, 89)( 45, 96)( 46, 97)( 47, 98)( 48, 93)( 49, 94)
( 50, 95)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)
(106,154)(107,155)(108,156)(109,157)(110,158)(111,162)(112,163)(113,164)
(114,159)(115,160)(116,161)(117,168)(118,169)(119,170)(120,165)(121,166)
(122,167)(123,171)(124,172)(125,173)(126,174)(127,175)(128,176)(129,177)
(130,178)(131,179)(132,180)(133,181)(134,182)(135,186)(136,187)(137,188)
(138,183)(139,184)(140,185)(141,192)(142,193)(143,194)(144,189)(145,190)
(146,191);
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)(147,168)(148,169)(149,170)
(150,165)(151,166)(152,167)(153,162)(154,163)(155,164)(156,159)(157,160)
(158,161)(171,192)(172,193)(173,194)(174,189)(175,190)(176,191)(177,186)
(178,187)(179,188)(180,183)(181,184)(182,185);
s3 := Sym(194)!( 3,123)( 4,125)( 5,124)( 6,126)( 7,128)( 8,127)( 9,132)
( 10,134)( 11,133)( 12,129)( 13,131)( 14,130)( 15,138)( 16,140)( 17,139)
( 18,135)( 19,137)( 20,136)( 21,141)( 22,143)( 23,142)( 24,144)( 25,146)
( 26,145)( 27, 99)( 28,101)( 29,100)( 30,102)( 31,104)( 32,103)( 33,108)
( 34,110)( 35,109)( 36,105)( 37,107)( 38,106)( 39,114)( 40,116)( 41,115)
( 42,111)( 43,113)( 44,112)( 45,117)( 46,119)( 47,118)( 48,120)( 49,122)
( 50,121)( 51,171)( 52,173)( 53,172)( 54,174)( 55,176)( 56,175)( 57,180)
( 58,182)( 59,181)( 60,177)( 61,179)( 62,178)( 63,186)( 64,188)( 65,187)
( 66,183)( 67,185)( 68,184)( 69,189)( 70,191)( 71,190)( 72,192)( 73,194)
( 74,193)( 75,147)( 76,149)( 77,148)( 78,150)( 79,152)( 80,151)( 81,156)
( 82,158)( 83,157)( 84,153)( 85,155)( 86,154)( 87,162)( 88,164)( 89,163)
( 90,159)( 91,161)( 92,160)( 93,165)( 94,167)( 95,166)( 96,168)( 97,170)
( 98,169);
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*s1*s2*s1*s2*s1*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope