Polytope of Type {2,6,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4,8}*768b
if this polytope has a name.
Group : SmallGroup(768,1036167)
Rank : 5
Schlafli Type : {2,6,4,8}
Number of vertices, edges, etc : 2, 6, 12, 16, 8
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 : {2,6,4,4}*384
3-fold quotients : {2,2,4,8}*256b
4-fold quotients : {2,6,2,4}*192, {2,6,4,2}*192a
6-fold quotients : {2,2,4,4}*128
8-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
12-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
16-fold quotients : {2,3,2,2}*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, 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)( 25, 50)( 26, 49)
( 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)( 73, 98)( 74, 97)
( 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)(121,146)(122,145)
(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)(169,194)(170,193);;
s2 := ( 3, 76)( 4, 75)( 5, 77)( 6, 79)( 7, 78)( 8, 80)( 9, 82)( 10, 81)
( 11, 83)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)( 18, 88)
( 19, 87)( 20, 89)( 21, 97)( 22, 96)( 23, 98)( 24, 94)( 25, 93)( 26, 95)
( 27, 52)( 28, 51)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 58)( 34, 57)
( 35, 59)( 36, 61)( 37, 60)( 38, 62)( 39, 67)( 40, 66)( 41, 68)( 42, 64)
( 43, 63)( 44, 65)( 45, 73)( 46, 72)( 47, 74)( 48, 70)( 49, 69)( 50, 71)
( 99,172)(100,171)(101,173)(102,175)(103,174)(104,176)(105,178)(106,177)
(107,179)(108,181)(109,180)(110,182)(111,187)(112,186)(113,188)(114,184)
(115,183)(116,185)(117,193)(118,192)(119,194)(120,190)(121,189)(122,191)
(123,148)(124,147)(125,149)(126,151)(127,150)(128,152)(129,154)(130,153)
(131,155)(132,157)(133,156)(134,158)(135,163)(136,162)(137,164)(138,160)
(139,159)(140,161)(141,169)(142,168)(143,170)(144,166)(145,165)(146,167);;
s3 := ( 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);;
s4 := ( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,108)( 10,109)
( 11,110)( 12,105)( 13,106)( 14,107)( 15,114)( 16,115)( 17,116)( 18,111)
( 19,112)( 20,113)( 21,117)( 22,118)( 23,119)( 24,120)( 25,121)( 26,122)
( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)( 33,132)( 34,133)
( 35,134)( 36,129)( 37,130)( 38,131)( 39,138)( 40,139)( 41,140)( 42,135)
( 43,136)( 44,137)( 45,141)( 46,142)( 47,143)( 48,144)( 49,145)( 50,146)
( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,156)( 58,157)
( 59,158)( 60,153)( 61,154)( 62,155)( 63,162)( 64,163)( 65,164)( 66,159)
( 67,160)( 68,161)( 69,165)( 70,166)( 71,167)( 72,168)( 73,169)( 74,170)
( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)( 80,176)( 81,180)( 82,181)
( 83,182)( 84,177)( 85,178)( 86,179)( 87,186)( 88,187)( 89,188)( 90,183)
( 91,184)( 92,185)( 93,189)( 94,190)( 95,191)( 96,192)( 97,193)( 98,194);;
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,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 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, 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)( 25, 50)
( 26, 49)( 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)( 73, 98)
( 74, 97)( 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)(121,146)
(122,145)(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)(169,194)
(170,193);
s2 := Sym(194)!( 3, 76)( 4, 75)( 5, 77)( 6, 79)( 7, 78)( 8, 80)( 9, 82)
( 10, 81)( 11, 83)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)
( 18, 88)( 19, 87)( 20, 89)( 21, 97)( 22, 96)( 23, 98)( 24, 94)( 25, 93)
( 26, 95)( 27, 52)( 28, 51)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 58)
( 34, 57)( 35, 59)( 36, 61)( 37, 60)( 38, 62)( 39, 67)( 40, 66)( 41, 68)
( 42, 64)( 43, 63)( 44, 65)( 45, 73)( 46, 72)( 47, 74)( 48, 70)( 49, 69)
( 50, 71)( 99,172)(100,171)(101,173)(102,175)(103,174)(104,176)(105,178)
(106,177)(107,179)(108,181)(109,180)(110,182)(111,187)(112,186)(113,188)
(114,184)(115,183)(116,185)(117,193)(118,192)(119,194)(120,190)(121,189)
(122,191)(123,148)(124,147)(125,149)(126,151)(127,150)(128,152)(129,154)
(130,153)(131,155)(132,157)(133,156)(134,158)(135,163)(136,162)(137,164)
(138,160)(139,159)(140,161)(141,169)(142,168)(143,170)(144,166)(145,165)
(146,167);
s3 := 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);
s4 := Sym(194)!( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,108)
( 10,109)( 11,110)( 12,105)( 13,106)( 14,107)( 15,114)( 16,115)( 17,116)
( 18,111)( 19,112)( 20,113)( 21,117)( 22,118)( 23,119)( 24,120)( 25,121)
( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)( 33,132)
( 34,133)( 35,134)( 36,129)( 37,130)( 38,131)( 39,138)( 40,139)( 41,140)
( 42,135)( 43,136)( 44,137)( 45,141)( 46,142)( 47,143)( 48,144)( 49,145)
( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,156)
( 58,157)( 59,158)( 60,153)( 61,154)( 62,155)( 63,162)( 64,163)( 65,164)
( 66,159)( 67,160)( 68,161)( 69,165)( 70,166)( 71,167)( 72,168)( 73,169)
( 74,170)( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)( 80,176)( 81,180)
( 82,181)( 83,182)( 84,177)( 85,178)( 86,179)( 87,186)( 88,187)( 89,188)
( 90,183)( 91,184)( 92,185)( 93,189)( 94,190)( 95,191)( 96,192)( 97,193)
( 98,194);
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, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope