Polytope of Type {2,8,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,12}*768a
if this polytope has a name.
Group : SmallGroup(768,141633)
Rank : 4
Schlafli Type : {2,8,12}
Number of vertices, edges, etc : 2, 16, 96, 24
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 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 : {2,4,12}*384a, {2,8,12}*384a, {2,8,12}*384b
3-fold quotients : {2,8,4}*256a
4-fold quotients : {2,4,12}*192a, {2,8,6}*192
6-fold quotients : {2,8,4}*128a, {2,8,4}*128b, {2,4,4}*128
8-fold quotients : {2,2,12}*96, {2,4,6}*96a
12-fold quotients : {2,4,4}*64, {2,8,2}*64
16-fold quotients : {2,2,6}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*32
32-fold quotients : {2,2,3}*24
48-fold quotients : {2,2,2}*16
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)
( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)( 33,123)( 34,124)
( 35,125)( 36,126)( 37,127)( 38,128)( 39,144)( 40,145)( 41,146)( 42,141)
( 43,142)( 44,143)( 45,138)( 46,139)( 47,140)( 48,135)( 49,136)( 50,137)
( 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)
( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,171)( 82,172)
( 83,173)( 84,174)( 85,175)( 86,176)( 87,192)( 88,193)( 89,194)( 90,189)
( 91,190)( 92,191)( 93,186)( 94,187)( 95,188)( 96,183)( 97,184)( 98,185);;
s2 := ( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 31, 38)( 32, 37)( 39, 45)( 40, 47)
( 41, 46)( 42, 48)( 43, 50)( 44, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)
( 55, 68)( 56, 67)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 61, 74)( 62, 73)
( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 87)( 82, 89)
( 83, 88)( 84, 90)( 85, 92)( 86, 91)( 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)(147,186)(148,188)(149,187)(150,183)
(151,185)(152,184)(153,192)(154,194)(155,193)(156,189)(157,191)(158,190)
(159,174)(160,176)(161,175)(162,171)(163,173)(164,172)(165,180)(166,182)
(167,181)(168,177)(169,179)(170,178);;
s3 := ( 3, 52)( 4, 51)( 5, 53)( 6, 55)( 7, 54)( 8, 56)( 9, 58)( 10, 57)
( 11, 59)( 12, 61)( 13, 60)( 14, 62)( 15, 64)( 16, 63)( 17, 65)( 18, 67)
( 19, 66)( 20, 68)( 21, 70)( 22, 69)( 23, 71)( 24, 73)( 25, 72)( 26, 74)
( 27, 79)( 28, 78)( 29, 80)( 30, 76)( 31, 75)( 32, 77)( 33, 85)( 34, 84)
( 35, 86)( 36, 82)( 37, 81)( 38, 83)( 39, 91)( 40, 90)( 41, 92)( 42, 88)
( 43, 87)( 44, 89)( 45, 97)( 46, 96)( 47, 98)( 48, 94)( 49, 93)( 50, 95)
( 99,148)(100,147)(101,149)(102,151)(103,150)(104,152)(105,154)(106,153)
(107,155)(108,157)(109,156)(110,158)(111,160)(112,159)(113,161)(114,163)
(115,162)(116,164)(117,166)(118,165)(119,167)(120,169)(121,168)(122,170)
(123,175)(124,174)(125,176)(126,172)(127,171)(128,173)(129,181)(130,180)
(131,182)(132,178)(133,177)(134,179)(135,187)(136,186)(137,188)(138,184)
(139,183)(140,185)(141,193)(142,192)(143,194)(144,190)(145,189)(146,191);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)( 33,123)
( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,144)( 40,145)( 41,146)
( 42,141)( 43,142)( 44,143)( 45,138)( 46,139)( 47,140)( 48,135)( 49,136)
( 50,137)( 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)( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,171)
( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,192)( 88,193)( 89,194)
( 90,189)( 91,190)( 92,191)( 93,186)( 94,187)( 95,188)( 96,183)( 97,184)
( 98,185);
s2 := Sym(194)!( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 31, 38)( 32, 37)( 39, 45)
( 40, 47)( 41, 46)( 42, 48)( 43, 50)( 44, 49)( 51, 63)( 52, 65)( 53, 64)
( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 61, 74)
( 62, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 87)
( 82, 89)( 83, 88)( 84, 90)( 85, 92)( 86, 91)( 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)(147,186)(148,188)(149,187)
(150,183)(151,185)(152,184)(153,192)(154,194)(155,193)(156,189)(157,191)
(158,190)(159,174)(160,176)(161,175)(162,171)(163,173)(164,172)(165,180)
(166,182)(167,181)(168,177)(169,179)(170,178);
s3 := Sym(194)!( 3, 52)( 4, 51)( 5, 53)( 6, 55)( 7, 54)( 8, 56)( 9, 58)
( 10, 57)( 11, 59)( 12, 61)( 13, 60)( 14, 62)( 15, 64)( 16, 63)( 17, 65)
( 18, 67)( 19, 66)( 20, 68)( 21, 70)( 22, 69)( 23, 71)( 24, 73)( 25, 72)
( 26, 74)( 27, 79)( 28, 78)( 29, 80)( 30, 76)( 31, 75)( 32, 77)( 33, 85)
( 34, 84)( 35, 86)( 36, 82)( 37, 81)( 38, 83)( 39, 91)( 40, 90)( 41, 92)
( 42, 88)( 43, 87)( 44, 89)( 45, 97)( 46, 96)( 47, 98)( 48, 94)( 49, 93)
( 50, 95)( 99,148)(100,147)(101,149)(102,151)(103,150)(104,152)(105,154)
(106,153)(107,155)(108,157)(109,156)(110,158)(111,160)(112,159)(113,161)
(114,163)(115,162)(116,164)(117,166)(118,165)(119,167)(120,169)(121,168)
(122,170)(123,175)(124,174)(125,176)(126,172)(127,171)(128,173)(129,181)
(130,180)(131,182)(132,178)(133,177)(134,179)(135,187)(136,186)(137,188)
(138,184)(139,183)(140,185)(141,193)(142,192)(143,194)(144,190)(145,189)
(146,191);
poly := sub<Sym(194)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope