Polytope of Type {2,16,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16,12}*768a
if this polytope has a name.
Group : SmallGroup(768,323305)
Rank : 4
Schlafli Type : {2,16,12}
Number of vertices, edges, etc : 2, 16, 96, 12
Order of s0s1s2s3 : 48
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 : {2,8,12}*384a, {2,16,6}*384
3-fold quotients : {2,16,4}*256a
4-fold quotients : {2,4,12}*192a, {2,8,6}*192
6-fold quotients : {2,8,4}*128a, {2,16,2}*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)( 9,108)( 10,109)
( 11,110)( 12,105)( 13,106)( 14,107)( 15,111)( 16,112)( 17,113)( 18,114)
( 19,115)( 20,116)( 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)( 39,141)( 40,142)( 41,143)( 42,144)
( 43,145)( 44,146)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)( 50,140)
( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,156)( 58,157)
( 59,158)( 60,153)( 61,154)( 62,155)( 63,159)( 64,160)( 65,161)( 66,162)
( 67,163)( 68,164)( 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)( 87,189)( 88,190)( 89,191)( 90,192)
( 91,193)( 92,194)( 93,183)( 94,184)( 95,185)( 96,186)( 97,187)( 98,188);;
s2 := ( 4, 5)( 7, 8)( 9, 12)( 10, 14)( 11, 13)( 16, 17)( 19, 20)( 21, 24)
( 22, 26)( 23, 25)( 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, 72)( 58, 74)( 59, 73)( 60, 69)
( 61, 71)( 62, 70)( 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)(105,132)(106,134)(107,133)(108,129)
(109,131)(110,130)(111,135)(112,137)(113,136)(114,138)(115,140)(116,139)
(117,144)(118,146)(119,145)(120,141)(121,143)(122,142)(147,183)(148,185)
(149,184)(150,186)(151,188)(152,187)(153,192)(154,194)(155,193)(156,189)
(157,191)(158,190)(159,171)(160,173)(161,172)(162,174)(163,176)(164,175)
(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, 76)( 28, 75)( 29, 77)( 30, 79)( 31, 78)( 32, 80)( 33, 82)( 34, 81)
( 35, 83)( 36, 85)( 37, 84)( 38, 86)( 39, 88)( 40, 87)( 41, 89)( 42, 91)
( 43, 90)( 44, 92)( 45, 94)( 46, 93)( 47, 95)( 48, 97)( 49, 96)( 50, 98)
( 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)
(123,172)(124,171)(125,173)(126,175)(127,174)(128,176)(129,178)(130,177)
(131,179)(132,181)(133,180)(134,182)(135,184)(136,183)(137,185)(138,187)
(139,186)(140,188)(141,190)(142,189)(143,191)(144,193)(145,192)(146,194);;
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,
s1*s2*s3*s2*s1*s2*s3*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 9,108)
( 10,109)( 11,110)( 12,105)( 13,106)( 14,107)( 15,111)( 16,112)( 17,113)
( 18,114)( 19,115)( 20,116)( 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)( 39,141)( 40,142)( 41,143)
( 42,144)( 43,145)( 44,146)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)
( 50,140)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,156)
( 58,157)( 59,158)( 60,153)( 61,154)( 62,155)( 63,159)( 64,160)( 65,161)
( 66,162)( 67,163)( 68,164)( 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)( 87,189)( 88,190)( 89,191)
( 90,192)( 91,193)( 92,194)( 93,183)( 94,184)( 95,185)( 96,186)( 97,187)
( 98,188);
s2 := Sym(194)!( 4, 5)( 7, 8)( 9, 12)( 10, 14)( 11, 13)( 16, 17)( 19, 20)
( 21, 24)( 22, 26)( 23, 25)( 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, 72)( 58, 74)( 59, 73)
( 60, 69)( 61, 71)( 62, 70)( 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)(105,132)(106,134)(107,133)
(108,129)(109,131)(110,130)(111,135)(112,137)(113,136)(114,138)(115,140)
(116,139)(117,144)(118,146)(119,145)(120,141)(121,143)(122,142)(147,183)
(148,185)(149,184)(150,186)(151,188)(152,187)(153,192)(154,194)(155,193)
(156,189)(157,191)(158,190)(159,171)(160,173)(161,172)(162,174)(163,176)
(164,175)(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, 76)( 28, 75)( 29, 77)( 30, 79)( 31, 78)( 32, 80)( 33, 82)
( 34, 81)( 35, 83)( 36, 85)( 37, 84)( 38, 86)( 39, 88)( 40, 87)( 41, 89)
( 42, 91)( 43, 90)( 44, 92)( 45, 94)( 46, 93)( 47, 95)( 48, 97)( 49, 96)
( 50, 98)( 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)(123,172)(124,171)(125,173)(126,175)(127,174)(128,176)(129,178)
(130,177)(131,179)(132,181)(133,180)(134,182)(135,184)(136,183)(137,185)
(138,187)(139,186)(140,188)(141,190)(142,189)(143,191)(144,193)(145,192)
(146,194);
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, s1*s2*s3*s2*s1*s2*s3*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope