Polytope of Type {8,6,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,4,2}*768a
if this polytope has a name.
Group : SmallGroup(768,1044756)
Rank : 5
Schlafli Type : {8,6,4,2}
Number of vertices, edges, etc : 8, 24, 12, 4, 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 : {4,6,4,2}*384a, {8,6,2,2}*384
3-fold quotients : {8,2,4,2}*256
4-fold quotients : {2,6,4,2}*192a, {4,6,2,2}*192a
6-fold quotients : {4,2,4,2}*128, {8,2,2,2}*128
8-fold quotients : {2,6,2,2}*96
12-fold quotients : {2,2,4,2}*64, {4,2,2,2}*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, 25)( 2, 26)( 3, 27)( 4, 28)( 5, 29)( 6, 30)( 7, 31)( 8, 32)
( 9, 33)( 10, 34)( 11, 35)( 12, 36)( 13, 40)( 14, 41)( 15, 42)( 16, 37)
( 17, 38)( 18, 39)( 19, 46)( 20, 47)( 21, 48)( 22, 43)( 23, 44)( 24, 45)
( 49, 73)( 50, 74)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)
( 57, 81)( 58, 82)( 59, 83)( 60, 84)( 61, 88)( 62, 89)( 63, 90)( 64, 85)
( 65, 86)( 66, 87)( 67, 94)( 68, 95)( 69, 96)( 70, 91)( 71, 92)( 72, 93)
( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)(103,127)(104,128)
(105,129)(106,130)(107,131)(108,132)(109,136)(110,137)(111,138)(112,133)
(113,134)(114,135)(115,142)(116,143)(117,144)(118,139)(119,140)(120,141)
(145,169)(146,170)(147,171)(148,172)(149,173)(150,174)(151,175)(152,176)
(153,177)(154,178)(155,179)(156,180)(157,184)(158,185)(159,186)(160,181)
(161,182)(162,183)(163,190)(164,191)(165,192)(166,187)(167,188)(168,189);;
s1 := ( 1, 97)( 2, 99)( 3, 98)( 4,100)( 5,102)( 6,101)( 7,103)( 8,105)
( 9,104)( 10,106)( 11,108)( 12,107)( 13,112)( 14,114)( 15,113)( 16,109)
( 17,111)( 18,110)( 19,118)( 20,120)( 21,119)( 22,115)( 23,117)( 24,116)
( 25,133)( 26,135)( 27,134)( 28,136)( 29,138)( 30,137)( 31,139)( 32,141)
( 33,140)( 34,142)( 35,144)( 36,143)( 37,121)( 38,123)( 39,122)( 40,124)
( 41,126)( 42,125)( 43,127)( 44,129)( 45,128)( 46,130)( 47,132)( 48,131)
( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)( 56,153)
( 57,152)( 58,154)( 59,156)( 60,155)( 61,160)( 62,162)( 63,161)( 64,157)
( 65,159)( 66,158)( 67,166)( 68,168)( 69,167)( 70,163)( 71,165)( 72,164)
( 73,181)( 74,183)( 75,182)( 76,184)( 77,186)( 78,185)( 79,187)( 80,189)
( 81,188)( 82,190)( 83,192)( 84,191)( 85,169)( 86,171)( 87,170)( 88,172)
( 89,174)( 90,173)( 91,175)( 92,177)( 93,176)( 94,178)( 95,180)( 96,179);;
s2 := ( 1, 38)( 2, 37)( 3, 39)( 4, 41)( 5, 40)( 6, 42)( 7, 44)( 8, 43)
( 9, 45)( 10, 47)( 11, 46)( 12, 48)( 13, 29)( 14, 28)( 15, 30)( 16, 26)
( 17, 25)( 18, 27)( 19, 35)( 20, 34)( 21, 36)( 22, 32)( 23, 31)( 24, 33)
( 49, 92)( 50, 91)( 51, 93)( 52, 95)( 53, 94)( 54, 96)( 55, 86)( 56, 85)
( 57, 87)( 58, 89)( 59, 88)( 60, 90)( 61, 83)( 62, 82)( 63, 84)( 64, 80)
( 65, 79)( 66, 81)( 67, 77)( 68, 76)( 69, 78)( 70, 74)( 71, 73)( 72, 75)
( 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)
(145,176)(146,175)(147,177)(148,179)(149,178)(150,180)(151,170)(152,169)
(153,171)(154,173)(155,172)(156,174)(157,188)(158,187)(159,189)(160,191)
(161,190)(162,192)(163,182)(164,181)(165,183)(166,185)(167,184)(168,186);;
s3 := ( 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, 61)( 14, 62)( 15, 63)( 16, 64)
( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)( 24, 72)
( 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, 85)( 38, 86)( 39, 87)( 40, 88)
( 41, 89)( 42, 90)( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)( 48, 96)
( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)
(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)(112,160)
(113,161)(114,162)(115,163)(116,164)(117,165)(118,166)(119,167)(120,168)
(121,169)(122,170)(123,171)(124,172)(125,173)(126,174)(127,175)(128,176)
(129,177)(130,178)(131,179)(132,180)(133,181)(134,182)(135,183)(136,184)
(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192);;
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*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!( 1, 25)( 2, 26)( 3, 27)( 4, 28)( 5, 29)( 6, 30)( 7, 31)
( 8, 32)( 9, 33)( 10, 34)( 11, 35)( 12, 36)( 13, 40)( 14, 41)( 15, 42)
( 16, 37)( 17, 38)( 18, 39)( 19, 46)( 20, 47)( 21, 48)( 22, 43)( 23, 44)
( 24, 45)( 49, 73)( 50, 74)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)
( 56, 80)( 57, 81)( 58, 82)( 59, 83)( 60, 84)( 61, 88)( 62, 89)( 63, 90)
( 64, 85)( 65, 86)( 66, 87)( 67, 94)( 68, 95)( 69, 96)( 70, 91)( 71, 92)
( 72, 93)( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)(103,127)
(104,128)(105,129)(106,130)(107,131)(108,132)(109,136)(110,137)(111,138)
(112,133)(113,134)(114,135)(115,142)(116,143)(117,144)(118,139)(119,140)
(120,141)(145,169)(146,170)(147,171)(148,172)(149,173)(150,174)(151,175)
(152,176)(153,177)(154,178)(155,179)(156,180)(157,184)(158,185)(159,186)
(160,181)(161,182)(162,183)(163,190)(164,191)(165,192)(166,187)(167,188)
(168,189);
s1 := Sym(194)!( 1, 97)( 2, 99)( 3, 98)( 4,100)( 5,102)( 6,101)( 7,103)
( 8,105)( 9,104)( 10,106)( 11,108)( 12,107)( 13,112)( 14,114)( 15,113)
( 16,109)( 17,111)( 18,110)( 19,118)( 20,120)( 21,119)( 22,115)( 23,117)
( 24,116)( 25,133)( 26,135)( 27,134)( 28,136)( 29,138)( 30,137)( 31,139)
( 32,141)( 33,140)( 34,142)( 35,144)( 36,143)( 37,121)( 38,123)( 39,122)
( 40,124)( 41,126)( 42,125)( 43,127)( 44,129)( 45,128)( 46,130)( 47,132)
( 48,131)( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)
( 56,153)( 57,152)( 58,154)( 59,156)( 60,155)( 61,160)( 62,162)( 63,161)
( 64,157)( 65,159)( 66,158)( 67,166)( 68,168)( 69,167)( 70,163)( 71,165)
( 72,164)( 73,181)( 74,183)( 75,182)( 76,184)( 77,186)( 78,185)( 79,187)
( 80,189)( 81,188)( 82,190)( 83,192)( 84,191)( 85,169)( 86,171)( 87,170)
( 88,172)( 89,174)( 90,173)( 91,175)( 92,177)( 93,176)( 94,178)( 95,180)
( 96,179);
s2 := Sym(194)!( 1, 38)( 2, 37)( 3, 39)( 4, 41)( 5, 40)( 6, 42)( 7, 44)
( 8, 43)( 9, 45)( 10, 47)( 11, 46)( 12, 48)( 13, 29)( 14, 28)( 15, 30)
( 16, 26)( 17, 25)( 18, 27)( 19, 35)( 20, 34)( 21, 36)( 22, 32)( 23, 31)
( 24, 33)( 49, 92)( 50, 91)( 51, 93)( 52, 95)( 53, 94)( 54, 96)( 55, 86)
( 56, 85)( 57, 87)( 58, 89)( 59, 88)( 60, 90)( 61, 83)( 62, 82)( 63, 84)
( 64, 80)( 65, 79)( 66, 81)( 67, 77)( 68, 76)( 69, 78)( 70, 74)( 71, 73)
( 72, 75)( 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)(145,176)(146,175)(147,177)(148,179)(149,178)(150,180)(151,170)
(152,169)(153,171)(154,173)(155,172)(156,174)(157,188)(158,187)(159,189)
(160,191)(161,190)(162,192)(163,182)(164,181)(165,183)(166,185)(167,184)
(168,186);
s3 := 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, 61)( 14, 62)( 15, 63)
( 16, 64)( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)
( 24, 72)( 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, 85)( 38, 86)( 39, 87)
( 40, 88)( 41, 89)( 42, 90)( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)
( 48, 96)( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)
(104,152)(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)
(112,160)(113,161)(114,162)(115,163)(116,164)(117,165)(118,166)(119,167)
(120,168)(121,169)(122,170)(123,171)(124,172)(125,173)(126,174)(127,175)
(128,176)(129,177)(130,178)(131,179)(132,180)(133,181)(134,182)(135,183)
(136,184)(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)
(144,192);
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*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope