Acronym | ranq | ||
Name |
rectified hecatonicosihexapentacosiheptacontihexaexon, equatorial cross-section of laq-first bay | ||
Circumradius | sqrt(2) = 1.414214 | ||
Inradius wrt. jak | 2/sqrt(3) = 1.154701 | ||
Inradius wrt. ril | 3/sqrt(7) = 1.133893 | ||
Inradius wrt. rag | 1 | ||
Lace city in approx. ASCII-art |
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R c r -- o3o3o *b3o3x3o (rag) H q T p h -- x3o3o *b3o3o3x (sochax) r x b X R -- tegum sum of o3x3o *b3o3o3o (brox) and o3o3o *b3o3o3u (u-gee) H q T p h -- x3o3o *b3o3o3x (sochax) R c r -- o3o3o *b3o3x3o (rag) | | | | +-- x3o3o3o3o *c3o (jak) | | | +---- o3x3o3o3o *c3o (rojak) | | +------ x3o3o3o3x *c3o (trim) | +-------- o3o3o3x3o *c3o (alt. rojak) +---------- o3o3o3o3x *c3o (alt. jak) where: h = x3o3o3o3o (hix) H = o3o3o3o3x (dual hix) r = o3x3o3o3o (rix) R = o3o3o3x3o (inv. rix) p = x3o3o3x3o (spix) q = o3x3o3o3x (inv. spix) c = x3o3o3o3x (scad) T = xo3xo3oo3ox3ox&#zu (u-laced tegum sum of 2 tixes) b = o3x3o3x3o (sibrid) | |||
Volume | 1053/70 = 15.042857 | ||
Surface | [812+35 sqrt(3)+57 sqrt(7)]/10 = 102.342960 | ||
Dihedral angles | |||
Face vector | 756, 12096, 44352, 70560, 48384, 11592, 758 | ||
Confer |
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External links |
Incidence matrix according to Dynkin symbol
o3o3o3o *c3o3x3o . . . . . . . | 756 ♦ 32 | 160 16 | 320 80 | 160 80 160 | 32 20 80 40 | 2 16 10 -----------------+-----+-------+------------+-------------+-------------------+---------------------+----------- . . . . . x . | 2 | 12096 | 10 1 | 30 10 | 20 10 30 | 5 5 20 10 | 1 5 5 -----------------+-----+-------+------------+-------------+-------------------+---------------------+----------- . . . . o3x . | 3 | 3 | 40320 * | 6 1 | 6 3 6 | 2 3 6 3 | 1 2 3 . . . . . x3o | 3 | 3 | * 4032 ♦ 0 10 | 0 0 30 | 0 0 20 10 | 0 5 5 -----------------+-----+-------+------------+-------------+-------------------+---------------------+----------- . . o . *c3o3x . ♦ 4 | 6 | 4 0 | 60480 * | 2 1 1 | 1 2 2 1 | 1 1 2 . . . . o3x3o ♦ 6 | 12 | 4 4 | * 10080 ♦ 0 0 6 | 0 0 6 3 | 0 2 3 -----------------+-----+-------+------------+-------------+-------------------+---------------------+----------- . o3o . *c3o3x . ♦ 5 | 10 | 10 0 | 5 0 | 24192 * * | 1 1 1 0 | 1 1 1 . . o3o *c3o3x . ♦ 5 | 10 | 10 0 | 5 0 | * 12096 * | 0 2 0 1 | 1 0 2 . . o . *c3o3x3o ♦ 10 | 30 | 20 10 | 5 5 | * * 12096 | 0 0 2 1 | 0 1 2 -----------------+-----+-------+------------+-------------+-------------------+---------------------+----------- o3o3o . *c3o3x . ♦ 6 | 15 | 20 0 | 15 0 | 6 0 0 | 4032 * * * | 1 1 0 . o3o3o *c3o3x . ♦ 10 | 40 | 80 0 | 80 0 | 16 16 0 | * 1512 * * | 1 0 1 . o3o . *c3o3x3o ♦ 15 | 60 | 60 20 | 30 15 | 6 0 6 | * * 4032 * | 0 1 1 . . o3o *c3o3x3o ♦ 15 | 60 | 60 20 | 30 15 | 0 6 6 | * * * 2016 | 0 0 2 -----------------+-----+-------+------------+-------------+-------------------+---------------------+----------- o3o3o3o *c3o3x . ♦ 27 | 216 | 720 0 | 1080 0 | 432 216 0 | 72 27 0 0 | 56 * * o3o3o . *c3o3x3o ♦ 21 | 105 | 140 35 | 105 35 | 42 0 21 | 7 0 7 0 | * 576 * . o3o3o *c3o3x3o ♦ 60 | 480 | 960 160 | 960 240 | 192 192 192 | 0 12 32 32 | * * 126
xoo3oxo3xoo3ooo3oox3oxo3oox&#zx → heights = 0 (tegum sum of 2 mutually inverted saroes and sabach) o..3o..3o..3o..3o..3o..3o.. & | 336 * ♦ 2 10 20 0 | 1 5 20 20 10 60 60 0 0 | 10 20 10 60 30 60 120 40 20 30 0 | 10 10 40 20 30 20 60 40 40 10 40 80 0 | 5 2 10 10 10 10 20 40 10 35 20 | 1 2 5 15 5 .o.3.o.3.o.3.o.3.o.3.o.3.o. | * 420 ♦ 0 0 16 16 | 0 0 0 8 16 24 96 8 24 | 0 0 8 48 24 16 96 96 48 48 16 | 0 0 48 24 16 4 32 48 48 32 48 96 4 | 0 0 12 16 4 8 16 48 12 32 24 | 0 2 6 16 4 ----------------------------------+---------+--------------------+----------------------------------------------+----------------------------------------------------------+---------------------------------------------------------------+--------------------------------------------------+---------------- x.. ... ... ... ... ... ... & | 2 0 | 336 * * * | 1 0 0 10 0 0 0 0 0 | 0 0 10 30 0 0 0 0 0 0 0 | 0 0 20 10 0 0 0 0 0 0 30 0 0 | 0 0 5 5 0 0 0 20 10 0 0 | 0 1 5 5 0 ... ... x.. ... ... ... ... & | 2 0 | * 1680 * * | 0 1 4 0 0 6 0 0 0 | 4 6 0 0 6 12 12 0 0 0 0 | 6 4 0 0 12 6 12 4 4 0 0 12 0 | 4 1 1 0 6 4 4 4 0 12 4 | 1 1 1 4 4 oo.3oo.3oo.3oo.3oo.3oo.3oo.&#x & | 1 1 | * * 6720 * | 0 0 0 1 1 3 6 0 0 | 0 0 1 6 3 3 12 6 3 6 0 | 0 0 6 3 3 1 6 6 6 2 9 18 0 | 0 0 3 2 1 2 3 12 3 8 6 | 0 1 3 5 2 ... .x. ... ... ... ... ... & | 0 2 | * * * 3360 | 0 0 0 0 1 0 6 1 3 | 0 0 1 3 3 0 6 12 6 6 3 | 0 0 6 3 3 0 2 6 6 6 9 18 1 | 0 0 3 3 1 2 2 12 3 8 6 | 0 1 3 5 2 ----------------------------------+---------+--------------------+----------------------------------------------+----------------------------------------------------------+---------------------------------------------------------------+--------------------------------------------------+---------------- x..3o.. ... ... ... ... ... & | 3 0 | 3 0 0 0 | 112 * * * * * * * * ♦ 0 0 10 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 30 0 0 | 0 0 0 0 0 0 0 20 10 0 0 | 0 0 5 5 0 ... o..3x.. ... ... ... ... & | 3 0 | 0 3 0 0 | * 560 * * * * * * * ♦ 4 0 0 0 6 0 0 0 0 0 0 | 6 0 0 0 12 0 0 0 0 0 0 12 0 | 4 0 0 0 6 0 0 4 0 12 4 | 1 0 1 4 4 ... ... x..3o.. ... ... ... & | 3 0 | 0 3 0 0 | * * 2240 * * * * * * | 1 3 0 0 0 3 0 0 0 0 0 | 3 3 0 0 3 3 3 0 0 0 0 0 0 | 3 1 0 0 3 3 1 0 0 3 0 | 1 1 0 1 3 xo. ... ... ... ... ... ...&#x & | 2 1 | 1 0 2 0 | * * * 3360 * * * * * | 0 0 1 6 0 0 0 0 0 0 0 | 0 0 6 3 0 0 0 0 0 0 6 0 0 | 0 0 3 2 0 0 0 6 3 0 0 | 0 1 3 2 0 ... ox. ... ... ... ... ...&#x & | 1 2 | 0 0 2 1 | * * * * 3360 * * * * ♦ 0 0 1 0 3 0 0 0 0 6 0 | 0 0 0 0 3 0 0 0 0 0 9 18 0 | 0 0 0 0 1 0 0 12 3 8 6 | 0 0 3 5 2 ... ... xo. ... ... ... ...&#x & | 2 1 | 0 1 2 0 | * * * * * 10080 * * * | 0 0 0 0 1 2 4 0 0 0 0 | 0 0 0 0 2 1 4 2 2 0 0 4 0 | 0 0 1 0 1 2 2 2 0 4 2 | 0 1 1 2 2 ... ... ... ... ... ox. ...&#x & | 1 2 | 0 0 2 1 | * * * * * * 20160 * * | 0 0 0 1 0 0 2 2 1 1 0 | 0 0 2 1 0 0 1 2 2 1 2 4 0 | 0 0 2 1 0 1 1 4 1 2 2 | 0 1 2 2 1 .o.3.x. ... ... ... ... ... & | 0 3 | 0 0 0 3 | * * * * * * * 1120 * | 0 0 1 0 0 0 0 0 6 0 0 | 0 0 0 3 0 0 0 0 6 0 6 0 0 | 0 0 3 0 0 0 2 6 3 0 0 | 0 1 3 2 0 ... .x.3.o. ... ... ... ... & | 0 3 | 0 0 0 3 | * * * * * * * * 3360 | 0 0 0 0 1 0 0 4 0 0 2 | 0 0 2 0 2 0 0 2 0 4 0 4 1 | 0 0 1 2 1 2 0 2 0 4 2 | 0 1 1 2 2 ----------------------------------+---------+--------------------+----------------------------------------------+----------------------------------------------------------+---------------------------------------------------------------+--------------------------------------------------+---------------- ... o..3x..3o.. ... ... ... & ♦ 6 0 | 0 12 0 0 | 0 4 4 0 0 0 0 0 0 | 560 * * * * * * * * * * ♦ 3 0 0 0 3 0 0 0 0 0 0 0 0 | 3 0 0 0 3 0 0 0 0 3 0 | 1 0 0 1 3 ... ... x..3o..3o.. ... ... & ♦ 4 0 | 0 6 0 0 | 0 0 4 0 0 0 0 0 0 | * 1680 * * * * * * * * * | 1 2 0 0 0 1 0 0 0 0 0 0 0 | 2 1 0 0 1 2 0 0 0 0 0 | 1 1 0 0 2 xo.3ox. ... ... ... ... ...&#x & ♦ 3 3 | 3 0 6 3 | 1 0 0 3 3 0 0 1 0 | * * 1120 * * * * * * * * ♦ 0 0 0 0 0 0 0 0 0 0 6 0 0 | 0 0 0 0 0 0 0 6 3 0 0 | 0 0 3 2 0 xo. ... ... ... ... ox. ...&#x & ♦ 2 2 | 1 0 4 1 | 0 0 0 2 0 0 2 0 0 | * * * 10080 * * * * * * * | 0 0 2 1 0 0 0 0 0 0 1 0 0 | 0 0 2 1 0 0 0 2 1 0 0 | 0 1 2 1 0 ... ox.3xo. ... ... ... ...&#x & ♦ 3 3 | 0 3 6 3 | 0 1 0 0 3 3 0 0 1 | * * * * 3360 * * * * * * ♦ 0 0 0 0 2 0 0 0 0 0 0 4 0 | 0 0 0 0 1 0 0 2 0 4 2 | 0 0 1 2 2 ... ... xo.3oo. ... ... ...&#x & ♦ 3 1 | 0 3 3 0 | 0 0 1 0 0 3 0 0 0 | * * * * * 6720 * * * * * | 0 0 0 0 1 1 2 0 0 0 0 0 0 | 0 0 0 0 1 2 1 0 0 2 0 | 0 1 0 1 2 ... ... xo. ... ... ox. ...&#x & ♦ 2 2 | 0 1 4 1 | 0 0 0 0 0 2 2 0 0 | * * * * * * 20160 * * * * | 0 0 0 0 0 0 1 1 1 0 0 1 0 | 0 0 1 0 0 1 1 1 0 1 1 | 0 1 1 1 1 ... ... ... ... oo.3ox. ...&#x & ♦ 1 3 | 0 0 3 3 | 0 0 0 0 0 0 3 0 1 | * * * * * * * 13440 * * * | 0 0 1 0 0 0 0 1 0 1 0 1 0 | 0 0 1 1 0 1 0 1 0 1 1 | 0 1 1 1 1 ... ... ... ... ... ox.3oo.&#x & ♦ 1 3 | 0 0 3 3 | 0 0 0 0 0 0 3 1 0 | * * * * * * * * 6720 * * | 0 0 0 1 0 0 0 0 2 0 1 0 0 | 0 0 2 0 0 0 1 2 1 0 0 | 0 1 2 1 0 ... oxo ... ... ... oxo ...&#xt ♦ 2 4 | 0 0 8 4 | 0 0 0 0 4 0 4 0 0 | * * * * * * * * * 5040 * ♦ 0 0 0 0 0 0 0 0 0 0 2 4 0 | 0 0 0 0 0 0 0 4 1 2 2 | 0 0 2 2 1 ... .x.3.o.3.o. ... ... ... & ♦ 0 4 | 0 0 0 6 | 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * 1680 | 0 0 0 0 1 0 0 0 0 2 0 0 1 | 0 0 0 1 1 2 0 0 0 2 0 | 0 1 0 1 2 ----------------------------------+---------+--------------------+----------------------------------------------+----------------------------------------------------------+---------------------------------------------------------------+--------------------------------------------------+---------------- ... o..3x..3o..3o.. ... ... & ♦ 10 0 | 0 30 0 0 | 0 10 20 0 0 0 0 0 0 | 5 5 0 0 0 0 0 0 0 0 0 | 336 * * * * * * * * * * * * | 2 0 0 0 1 0 0 0 0 0 0 | 1 0 0 0 2 ... ... x..3o..3o..3o.. ... & ♦ 5 0 | 0 10 0 0 | 0 0 10 0 0 0 0 0 0 | 0 5 0 0 0 0 0 0 0 0 0 | * 672 * * * * * * * * * * * | 1 1 0 0 0 1 0 0 0 0 0 | 1 1 0 0 1 xo. ... ... ... oo.3ox. ...&#x & ♦ 2 3 | 1 0 6 3 | 0 0 0 3 0 0 6 0 1 | 0 0 0 3 0 0 0 2 0 0 0 | * * 6720 * * * * * * * * * * | 0 0 1 1 0 0 0 1 0 0 0 | 0 1 1 1 0 xo. ... ... ... ... ox.3oo.&#x & ♦ 2 3 | 1 0 6 3 | 0 0 0 3 0 0 6 1 0 | 0 0 0 3 0 0 0 0 2 0 0 | * * * 3360 * * * * * * * * * | 0 0 2 0 0 0 0 0 1 0 0 | 0 1 2 0 0 ... ox.3xo.3oo. ... ... ...&#x & ♦ 6 4 | 0 12 12 6 | 0 4 4 0 6 12 0 0 4 | 1 0 0 0 4 4 0 0 0 0 1 | * * * * 1680 * * * * * * * * | 0 0 0 0 1 0 0 0 0 2 0 | 0 0 0 1 2 ... ... xo.3oo.3oo. ... ...&#x & ♦ 4 1 | 0 6 4 0 | 0 0 4 0 0 6 0 0 0 | 0 1 0 0 0 4 0 0 0 0 0 | * * * * * 1680 * * * * * * * | 0 0 0 0 1 2 0 0 0 0 0 | 0 1 0 0 2 ... ... xo.3oo. ... ox. ...&#x & ♦ 3 2 | 0 3 6 1 | 0 0 1 0 0 6 3 0 0 | 0 0 0 0 0 2 3 0 0 0 0 | * * * * * * 6720 * * * * * * | 0 0 0 0 0 1 1 0 0 1 0 | 0 1 0 1 1 ... ... xo. ... oo.3ox. ...&#x & ♦ 2 3 | 0 1 6 3 | 0 0 0 0 0 3 6 0 1 | 0 0 0 0 0 0 3 2 0 0 0 | * * * * * * * 6720 * * * * * | 0 0 1 0 0 1 0 0 0 0 1 | 0 1 1 0 1 ... ... xo. ... ... ox.3oo.&#x & ♦ 2 3 | 0 1 6 3 | 0 0 0 0 0 3 6 1 0 | 0 0 0 0 0 0 3 0 2 0 0 | * * * * * * * * 6720 * * * * | 0 0 1 0 0 0 1 1 0 0 0 | 0 1 1 1 0 ... ... ... oo.3oo.3ox. ...&#x & ♦ 1 4 | 0 0 4 6 | 0 0 0 0 0 0 6 0 4 | 0 0 0 0 0 0 0 4 0 0 1 | * * * * * * * * * 3360 * * * | 0 0 0 1 0 1 0 0 0 1 0 | 0 1 0 1 1 xoo3oxo ... ... ... oxo ...&#xt & ♦ 4 6 | 3 0 18 9 | 1 0 0 6 9 0 12 2 0 | 0 0 2 3 0 0 0 0 2 3 0 | * * * * * * * * * * 3360 * * | 0 0 0 0 0 0 0 2 1 0 0 | 0 0 2 1 0 ... oxo3xoo ... ... oxo ...&#xt & ♦ 4 6 | 0 3 18 9 | 0 1 0 0 9 6 12 0 2 | 0 0 0 0 2 0 3 2 0 3 0 | * * * * * * * * * * * 6720 * | 0 0 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1 ... .x.3.o.3.o.3.o. ... ... & ♦ 0 5 | 0 0 0 10 | 0 0 0 0 0 0 0 0 10 | 0 0 0 0 0 0 0 0 0 0 5 | * * * * * * * * * * * * 336 | 0 0 0 0 1 2 0 0 0 0 0 | 0 1 0 0 2 ----------------------------------+---------+--------------------+----------------------------------------------+----------------------------------------------------------+---------------------------------------------------------------+--------------------------------------------------+---------------- ... o..3x..3o..3o..3o.. ... & ♦ 15 0 | 0 60 0 0 | 0 20 60 0 0 0 0 0 0 | 15 30 0 0 0 0 0 0 0 0 0 | 6 6 0 0 0 0 0 0 0 0 0 0 0 | 112 * * * * * * * * * * | 1 0 0 0 1 ... ... x..3o..3o..3o..3o.. & ♦ 6 0 | 0 15 0 0 | 0 0 20 0 0 0 0 0 0 | 0 15 0 0 0 0 0 0 0 0 0 | 0 6 0 0 0 0 0 0 0 0 0 0 0 | * 112 * * * * * * * * * | 1 1 0 0 0 xo. ... xo. ... oo.3ox.3oo.&#zx & ♦ 4 6 | 2 2 24 12 | 0 0 0 12 0 12 48 4 4 | 0 0 0 24 0 0 24 16 16 0 0 | 0 0 8 8 0 0 0 8 8 0 0 0 0 | * * 840 * * * * * * * * | 0 1 1 0 0 xo. ... ... oo.3oo.3ox. ...&#x & ♦ 2 4 | 1 0 8 6 | 0 0 0 4 0 0 12 0 4 | 0 0 0 6 0 0 0 8 0 0 1 | 0 0 4 0 0 0 0 0 0 2 0 0 0 | * * * 1680 * * * * * * * | 0 1 0 1 0 ... ox.3xo.3oo.3oo. ... ...&#x & ♦ 10 5 | 0 30 20 10 | 0 10 20 0 10 30 0 0 10 | 5 5 0 0 10 20 0 0 0 0 5 | 1 0 0 0 5 5 0 0 0 0 0 0 1 | * * * * 336 * * * * * * | 0 0 0 0 2 ... ... xo.3oo.3oo.3ox. ...&#x & ♦ 5 5 | 0 10 20 10 | 0 0 10 0 0 30 30 0 10 | 0 5 0 0 0 20 30 20 0 0 5 | 0 1 0 0 0 5 10 10 0 5 0 0 1 | * * * * * 672 * * * * * | 0 1 0 0 1 ... ... xo.3oo. ... ox.3oo.&#x & ♦ 3 3 | 0 3 9 3 | 0 0 1 0 0 9 9 1 0 | 0 0 0 0 0 3 9 0 3 0 0 | 0 0 0 0 0 0 3 0 3 0 0 0 0 | * * * * * * 2240 * * * * | 0 1 0 1 0 xoo3oxo ... ... oox3oxo ...&#xt & ♦ 6 9 | 3 3 36 18 | 1 1 0 9 18 9 36 3 3 | 0 0 3 9 3 0 9 6 6 9 0 | 0 0 3 0 0 0 0 0 3 0 3 3 0 | * * * * * * * 2240 * * * | 0 0 1 1 0 xoo3oxo ... ... ... oxo3oox&#xt ♦ 6 9 | 6 0 36 18 | 2 0 0 18 18 0 36 6 0 | 0 0 6 18 0 0 0 0 12 9 0 | 0 0 0 6 0 0 0 0 0 0 6 0 0 | * * * * * * * * 560 * * | 0 0 2 0 0 ... oxo3xoo3ooo ... oxo ...&#xt & ♦ 7 8 | 0 12 32 16 | 0 4 4 0 16 24 24 0 8 | 1 0 0 0 8 8 12 8 0 6 2 | 0 0 0 0 2 0 4 0 0 2 0 4 0 | * * * * * * * * * 1680 * | 0 0 0 1 1 ... oxo3xoo ... oox3oxo ...&#xt ♦ 6 9 | 0 6 36 18 | 0 2 0 0 18 18 36 0 6 | 0 0 0 0 6 0 18 12 0 9 0 | 0 0 0 0 0 0 0 6 0 0 0 6 0 | * * * * * * * * * * 1120 | 0 0 1 0 1 ----------------------------------+---------+--------------------+----------------------------------------------+----------------------------------------------------------+---------------------------------------------------------------+--------------------------------------------------+---------------- ... o..3x..3o..3o..3o..3o.. & ♦ 21 0 | 0 105 0 0 | 0 35 140 0 0 0 0 0 0 | 35 105 0 0 0 0 0 0 0 0 0 | 21 42 0 0 0 0 0 0 0 0 0 0 0 | 7 7 0 0 0 0 0 0 0 0 0 | 16 * * * * xo. ... xo.3oo.3oo.3ox.3oo.&#zx & ♦ 12 15 | 6 30 120 60 | 0 0 40 60 0 180 360 20 60 | 0 30 0 180 0 120 360 240 120 0 30 | 0 12 120 60 0 30 120 120 120 60 0 0 6 | 0 2 15 30 0 12 40 0 0 0 0 | * 56 * * * xoo3oxo3xoo ... oox3oxo3oox&#zx ♦ 24 36 | 24 24 288 144 | 8 8 0 144 144 144 576 48 48 | 0 0 48 288 48 0 288 192 192 144 0 | 0 0 96 96 0 0 0 96 96 0 96 96 0 | 0 0 12 0 0 0 0 32 16 0 16 | * * 70 * * xoo3oxo ... ooo3oox3oxo ...&#xt & ♦ 9 12 | 3 12 60 30 | 1 4 4 12 30 36 72 4 12 | 1 0 4 18 12 12 36 24 12 18 3 | 0 0 12 0 3 0 12 0 12 6 6 12 0 | 0 0 0 3 0 0 4 4 0 3 0 | * * * 560 * ... oxo3xoo3ooo3oox3oxo ...&#xt ♦ 30 30 | 0 120 240 120 | 0 40 120 0 120 360 360 0 120 | 30 60 0 0 120 240 360 240 0 90 60 | 12 12 0 0 60 60 120 120 0 60 0 120 12 | 2 0 0 0 12 12 0 0 0 30 20 | * * * * 56
xoxoo3oxooo3ooooo3oooxo3ooxox *c3ooooo&#xt → all heights = 1/sqrt(3) = 0.577350 (jak || rojak || trim || alt. rojak || alt. jak) ...
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