Polytope of Type {224}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {224}*448
Also Known As : 224-gon, {224}. if this polytope has another name.
Group : SmallGroup(448,5)
Rank : 2
Schlafli Type : {224}
Number of vertices, edges, etc : 224, 224
Order of s0s1 : 224
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{224,2} of size 896
{224,4} of size 1792
{224,4} of size 1792
Vertex Figure Of :
{2,224} of size 896
{4,224} of size 1792
{4,224} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {112}*224
4-fold quotients : {56}*112
7-fold quotients : {32}*64
8-fold quotients : {28}*56
14-fold quotients : {16}*32
16-fold quotients : {14}*28
28-fold quotients : {8}*16
32-fold quotients : {7}*14
56-fold quotients : {4}*8
112-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {448}*896
3-fold covers : {672}*1344
4-fold covers : {896}*1792
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 15, 22)( 16, 28)
( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 29, 43)( 30, 49)( 31, 48)
( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 36, 50)( 37, 56)( 38, 55)( 39, 54)
( 40, 53)( 41, 52)( 42, 51)( 57, 85)( 58, 91)( 59, 90)( 60, 89)( 61, 88)
( 62, 87)( 63, 86)( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)
( 70, 93)( 71,106)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)( 77,107)
( 78, 99)( 79,105)( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)(113,169)
(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,176)(121,182)
(122,181)(123,180)(124,179)(125,178)(126,177)(127,190)(128,196)(129,195)
(130,194)(131,193)(132,192)(133,191)(134,183)(135,189)(136,188)(137,187)
(138,186)(139,185)(140,184)(141,211)(142,217)(143,216)(144,215)(145,214)
(146,213)(147,212)(148,218)(149,224)(150,223)(151,222)(152,221)(153,220)
(154,219)(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)
(162,204)(163,210)(164,209)(165,208)(166,207)(167,206)(168,205);;
s1 := ( 1,114)( 2,113)( 3,119)( 4,118)( 5,117)( 6,116)( 7,115)( 8,121)
( 9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,135)( 16,134)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,136)( 22,128)( 23,127)( 24,133)
( 25,132)( 26,131)( 27,130)( 28,129)( 29,156)( 30,155)( 31,161)( 32,160)
( 33,159)( 34,158)( 35,157)( 36,163)( 37,162)( 38,168)( 39,167)( 40,166)
( 41,165)( 42,164)( 43,142)( 44,141)( 45,147)( 46,146)( 47,145)( 48,144)
( 49,143)( 50,149)( 51,148)( 52,154)( 53,153)( 54,152)( 55,151)( 56,150)
( 57,198)( 58,197)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)( 64,205)
( 65,204)( 66,210)( 67,209)( 68,208)( 69,207)( 70,206)( 71,219)( 72,218)
( 73,224)( 74,223)( 75,222)( 76,221)( 77,220)( 78,212)( 79,211)( 80,217)
( 81,216)( 82,215)( 83,214)( 84,213)( 85,170)( 86,169)( 87,175)( 88,174)
( 89,173)( 90,172)( 91,171)( 92,177)( 93,176)( 94,182)( 95,181)( 96,180)
( 97,179)( 98,178)( 99,191)(100,190)(101,196)(102,195)(103,194)(104,193)
(105,192)(106,184)(107,183)(108,189)(109,188)(110,187)(111,186)(112,185);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(224)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 15, 22)
( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 29, 43)( 30, 49)
( 31, 48)( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 36, 50)( 37, 56)( 38, 55)
( 39, 54)( 40, 53)( 41, 52)( 42, 51)( 57, 85)( 58, 91)( 59, 90)( 60, 89)
( 61, 88)( 62, 87)( 63, 86)( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)
( 69, 94)( 70, 93)( 71,106)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)
( 77,107)( 78, 99)( 79,105)( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)
(113,169)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,176)
(121,182)(122,181)(123,180)(124,179)(125,178)(126,177)(127,190)(128,196)
(129,195)(130,194)(131,193)(132,192)(133,191)(134,183)(135,189)(136,188)
(137,187)(138,186)(139,185)(140,184)(141,211)(142,217)(143,216)(144,215)
(145,214)(146,213)(147,212)(148,218)(149,224)(150,223)(151,222)(152,221)
(153,220)(154,219)(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)
(161,198)(162,204)(163,210)(164,209)(165,208)(166,207)(167,206)(168,205);
s1 := Sym(224)!( 1,114)( 2,113)( 3,119)( 4,118)( 5,117)( 6,116)( 7,115)
( 8,121)( 9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,135)
( 16,134)( 17,140)( 18,139)( 19,138)( 20,137)( 21,136)( 22,128)( 23,127)
( 24,133)( 25,132)( 26,131)( 27,130)( 28,129)( 29,156)( 30,155)( 31,161)
( 32,160)( 33,159)( 34,158)( 35,157)( 36,163)( 37,162)( 38,168)( 39,167)
( 40,166)( 41,165)( 42,164)( 43,142)( 44,141)( 45,147)( 46,146)( 47,145)
( 48,144)( 49,143)( 50,149)( 51,148)( 52,154)( 53,153)( 54,152)( 55,151)
( 56,150)( 57,198)( 58,197)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)
( 64,205)( 65,204)( 66,210)( 67,209)( 68,208)( 69,207)( 70,206)( 71,219)
( 72,218)( 73,224)( 74,223)( 75,222)( 76,221)( 77,220)( 78,212)( 79,211)
( 80,217)( 81,216)( 82,215)( 83,214)( 84,213)( 85,170)( 86,169)( 87,175)
( 88,174)( 89,173)( 90,172)( 91,171)( 92,177)( 93,176)( 94,182)( 95,181)
( 96,180)( 97,179)( 98,178)( 99,191)(100,190)(101,196)(102,195)(103,194)
(104,193)(105,192)(106,184)(107,183)(108,189)(109,188)(110,187)(111,186)
(112,185);
poly := sub<Sym(224)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
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