| Acronym | tridafupap |
| Name |
trigonal-duoantifastegiaprismatic alterprism, trigonal-duoantifastegiaprism atop lacing-ortho trigonal-duoantifastegiaprism |
| Circumradius | sqrt(7/8) = 0.935414 |
|
Lace city in approx. ASCII-art |
x3o x3o x3o o3x
(1) (3)
o3x x3o o3x o3x
(2) (4)
|
| Face vector | 36, 216, 492, 552, 328, 102, 16 |
| Confer |
|
Incidence matrix according to Dynkin symbol
xo3ox xx3oo &#x || xo3ox oo3xx &#x → height(1,2) = height(1,3) = height(2,4) = height(3,4) = sqrt(2/3) = 0.816497 = height of oct height(1,4) = height(2,3) = 1/sqrt(3) = 0.577350 = height of tridafup (tridafup || lacing-ortho tridafup) o.3o. o.3o. .. .. .. .. & | 36 | 2 2 2 2 4 | 1 4 1 3 4 4 3 6 6 12 | 2 2 1 6 2 2 6 1 2 5 4 2 10 8 10 8 4 | 1 2 3 3 2 3 3 6 8 7 7 5 6 6 6 | 1 1 1 5 4 5 4 2 9 2 | 3 3 3 ------------------------------------+----+----------------+--------------------------------+--------------------------------------------------+-------------------------------------------+--------------------------+------ x. .. .. .. .. .. .. .. & | 2 | 36 * * * * | 1 2 0 1 0 2 0 2 0 0 | 2 1 1 2 0 2 3 0 2 2 1 0 4 2 0 0 0 | 1 2 1 3 1 3 1 6 3 3 2 1 0 2 0 | 1 1 1 5 4 2 1 2 3 0 | 3 3 1 .. .. x. .. .. .. .. .. & | 2 | * 36 * * * | 0 2 1 0 2 0 1 0 2 0 | 1 2 0 3 2 0 2 1 0 2 1 2 0 0 4 2 0 | 1 1 3 1 2 1 3 0 3 2 3 1 6 0 2 | 1 1 1 2 1 5 4 0 3 2 | 3 1 3 oo3oo oo3oo &#x .. .. .. .. & | 2 | * * 36 * * | 0 0 0 2 2 0 0 0 0 4 | 0 0 1 4 1 0 0 0 0 0 0 0 4 4 4 2 2 | 0 2 2 0 0 0 0 4 4 2 4 2 2 4 3 | 1 0 0 4 4 2 2 2 6 1 | 2 3 2 o.3o. o.3o. || o.3o. o.3o. & | 2 | * * * 36 * | 0 0 0 0 0 2 2 0 0 4 | 0 0 0 0 0 1 4 1 0 0 0 0 4 2 4 4 2 | 0 0 0 2 2 0 0 2 4 4 2 2 4 3 4 | 0 1 0 2 2 4 2 1 6 2 | 2 2 3 o.3o. o.3o. || .o3.o .o3.o & | 2 | * * * * 72 | 0 0 0 0 0 0 0 2 2 2 | 0 0 0 0 0 0 0 0 1 2 2 1 2 2 2 2 1 | 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 | 0 0 1 2 2 2 2 1 4 1 | 2 2 2 ------------------------------------+----+----------------+--------------------------------+--------------------------------------------------+-------------------------------------------+--------------------------+------ x.3o. .. .. .. .. .. .. & | 3 | 3 0 0 0 0 | 12 * * * * * * * * * | 2 0 1 0 0 2 0 0 2 0 0 0 0 0 0 0 0 | 1 2 0 3 0 3 0 6 0 0 0 0 0 0 0 | 1 1 1 5 4 0 0 2 0 0 | 3 3 0 x. .. x. .. .. .. .. .. & | 4 | 2 2 0 0 0 | * 36 * * * * * * * * | 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 | 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 | 1 1 1 2 1 2 1 0 1 0 | 3 1 1 .. .. x.3o. .. .. .. .. & | 3 | 0 3 0 0 0 | * * 12 * * * * * * * | 0 2 0 0 2 0 0 1 0 0 0 2 0 0 0 0 0 | 1 0 3 0 2 0 3 0 0 0 0 0 6 0 0 | 1 1 1 0 0 5 4 0 0 2 | 3 0 3 xo .. .. .. &#x .. .. .. .. & | 3 | 1 0 2 0 0 | * * * 36 * * * * * * | 0 0 1 2 0 0 0 0 0 0 0 0 2 2 0 0 0 | 0 2 1 0 0 0 0 4 2 1 2 1 0 2 0 | 1 0 0 4 2 1 1 2 3 0 | 2 3 1 .. .. xx .. &#x .. .. .. .. & | 4 | 0 2 2 0 0 | * * * * 36 * * * * * | 0 0 0 2 1 0 0 0 0 0 0 0 0 0 2 0 0 | 0 1 2 0 0 0 0 0 2 0 2 0 2 0 1 | 1 0 0 2 0 2 2 0 2 1 | 2 1 2 x. .. .. .. || x. .. .. .. & | 4 | 2 0 0 2 0 | * * * * * 36 * * * * | 0 0 0 0 0 1 2 0 0 0 0 0 2 0 0 0 0 | 0 0 0 2 1 0 0 2 2 2 0 0 0 1 0 | 0 1 0 2 2 2 0 1 2 0 | 2 2 1 .. .. x. .. || .. .. o. .. & | 3 | 0 1 0 2 0 | * * * * * * 36 * * * | 0 0 0 0 0 0 2 1 0 0 0 0 0 0 2 2 0 | 0 0 0 1 2 0 0 0 2 2 1 1 4 0 2 | 0 1 0 1 1 4 2 0 3 2 | 2 1 3 x. .. .. .. || .o .. .. .. & | 3 | 1 0 0 0 2 | * * * * * * * 72 * * | 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 | 0 0 0 0 0 2 1 2 1 1 1 1 0 1 0 | 0 0 1 2 2 1 1 1 2 0 | 2 2 1 .. .. x. .. || .. .. .o .. & | 3 | 0 1 0 0 2 | * * * * * * * * 72 * | 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 | 0 0 0 0 0 1 2 0 1 1 1 1 2 0 1 | 0 0 1 1 1 2 2 0 2 1 | 2 1 2 oo3oo oo3oo &#x || o.3o. o.3o. & | 3 | 0 0 1 1 1 | * * * * * * * * * 144 | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 | 0 0 0 0 0 0 0 1 1 1 1 1 1 2 2 | 0 0 0 1 1 1 1 1 4 1 | 1 2 2 ------------------------------------+----+----------------+--------------------------------+--------------------------------------------------+-------------------------------------------+--------------------------+------ x.3o. x. .. .. .. .. .. & ♦ 6 | 6 3 0 0 0 | 2 3 0 0 0 0 0 0 0 0 | 12 * * * * * * * * * * * * * * * * | 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 | 1 1 1 2 1 0 0 0 0 0 | 3 1 0 x. .. x.3o. .. .. .. .. & ♦ 6 | 3 6 0 0 0 | 0 3 2 0 0 0 0 0 0 0 | * 12 * * * * * * * * * * * * * * * | 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 2 1 0 0 0 | 3 0 1 xo3ox .. .. &#x .. .. .. .. & ♦ 6 | 6 0 6 0 0 | 2 0 0 6 0 0 0 0 0 0 | * * 6 * * * * * * * * * * * * * * | 0 2 0 0 0 0 0 4 0 0 0 0 0 0 0 | 1 0 0 4 2 0 0 2 0 0 | 2 3 0 xo .. xx .. &#x .. .. .. .. & ♦ 6 | 2 3 4 0 0 | 0 1 0 2 2 0 0 0 0 0 | * * * 36 * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 | 1 0 0 2 0 1 1 0 1 0 | 2 1 1 .. .. xx3oo &#x .. .. .. .. & ♦ 6 | 0 6 3 0 0 | 0 0 2 0 3 0 0 0 0 0 | * * * * 12 * * * * * * * * * * * * | 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 | 1 0 0 0 0 2 2 0 0 1 | 2 0 2 x.3o. .. .. || x.3o. .. .. & ♦ 6 | 6 0 0 3 0 | 2 0 0 0 0 3 0 0 0 0 | * * * * * 12 * * * * * * * * * * * | 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 | 0 1 0 2 2 0 0 1 0 0 | 2 2 0 x. .. x. .. || x. .. o. .. & ♦ 6 | 3 2 0 4 0 | 0 1 0 0 0 2 2 0 0 0 | * * * * * * 36 * * * * * * * * * * | 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 | 0 1 0 1 1 2 0 0 1 0 | 2 1 1 .. .. x.3o. || .. .. o.3x. & ♦ 6 | 0 6 0 6 0 | 0 0 2 0 0 0 6 0 0 0 | * * * * * * * 6 * * * * * * * * * | 0 0 0 0 2 0 0 0 0 0 0 0 4 0 0 | 0 1 0 0 0 4 2 0 0 2 | 2 0 3 x.3o. .. .. || .o3.x .. .. & ♦ 6 | 6 0 0 0 6 | 2 0 0 0 0 0 0 6 0 0 | * * * * * * * * 12 * * * * * * * * | 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 | 0 0 1 2 2 0 0 1 0 0 | 2 2 0 x. .. x. .. || .o .. .o .. & ♦ 5 | 2 2 0 0 4 | 0 1 0 0 0 0 0 2 2 0 | * * * * * * * * * 36 * * * * * * * | 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 | 0 0 1 1 1 1 1 0 1 0 | 2 1 1 x. .. .. o. || .o .. .. .x & ♦ 4 | 1 1 0 0 4 | 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * 36 * * * * * * | 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 | 0 0 1 1 1 1 1 0 1 0 | 2 1 1 .. .. x.3o. || .. .. .o3.x & ♦ 6 | 0 6 0 0 6 | 0 0 2 0 0 0 0 0 6 0 | * * * * * * * * * * * 12 * * * * * | 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 | 0 0 1 0 0 2 2 0 0 1 | 2 0 2 xo .. .. .. &#x || x. .. .. .. & ♦ 5 | 2 0 2 2 2 | 0 0 0 1 0 1 0 1 0 2 | * * * * * * * * * * * * 72 * * * * | 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 | 0 0 0 1 1 1 0 1 2 0 | 1 2 1 .. ox .. .. &#x || .. o. .. .. & ♦ 4 | 1 0 2 1 2 | 0 0 0 1 0 0 0 1 0 2 | * * * * * * * * * * * * * 72 * * * | 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 | 0 0 0 1 1 0 1 1 2 0 | 1 2 1 .. .. xx .. &#x || .. .. o. .. & ♦ 5 | 0 2 2 2 2 | 0 0 0 0 1 0 1 0 1 2 | * * * * * * * * * * * * * * 72 * * | 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 | 0 0 0 1 0 1 1 0 2 1 | 1 1 2 .. .. .. oo &#x || .. .. .. x. & ♦ 4 | 0 1 1 2 2 | 0 0 0 0 0 0 1 0 1 2 | * * * * * * * * * * * * * * * 72 * | 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 | 0 0 0 0 1 1 1 0 2 1 | 1 1 2 oo3oo oo3oo &#x || oo3oo oo3oo &#x ♦ 4 | 0 0 2 2 2 | 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * * * * 36 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 0 1 4 1 | 0 2 2 ------------------------------------+----+----------------+--------------------------------+--------------------------------------------------+-------------------------------------------+--------------------------+------ x.3o. x.3o. .. .. .. .. & ♦ 9 | 9 9 0 0 0 | 3 9 3 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 3 0 0 xo3ox xx .. &#x .. .. .. .. & ♦ 12 | 12 6 12 0 0 | 4 6 0 12 6 0 0 0 0 0 | 2 0 2 6 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 6 * * * * * * * * * * * * * | 1 0 0 2 0 0 0 0 0 0 | 2 1 0 xo .. xx3oo &#x .. .. .. .. & ♦ 9 | 3 9 6 0 0 | 0 3 3 3 6 0 0 0 0 0 | 0 1 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 | * * 12 * * * * * * * * * * * * | 1 0 0 0 0 1 1 0 0 0 | 2 0 1 x.3o. x. .. || x.3o. o. .. & ♦ 9 | 9 3 0 6 0 | 3 3 0 0 0 6 3 0 0 0 | 1 0 0 0 0 2 3 0 0 0 0 0 0 0 0 0 0 | * * * 12 * * * * * * * * * * * | 0 1 0 1 1 0 0 0 0 0 | 2 1 0 x. .. x.3o. || x. .. o.3x. & ♦ 12 | 6 12 0 12 0 | 0 6 4 0 0 6 12 0 0 0 | 0 2 0 0 0 0 6 2 0 0 0 0 0 0 0 0 0 | * * * * 6 * * * * * * * * * * | 0 1 0 0 0 2 0 0 0 0 | 2 0 1 x.3o. x. .. || .o3.x .o .. & ♦ 9 | 9 3 0 0 12 | 3 3 0 0 0 0 0 12 6 0 | 1 0 0 0 0 0 0 0 2 3 3 0 0 0 0 0 0 | * * * * * 12 * * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 | 2 1 0 x. .. x.3o. || .o .. .o3.x & ♦ 9 | 3 9 0 0 12 | 0 3 3 0 0 0 0 6 12 0 | 0 1 0 0 0 0 0 0 0 3 3 2 0 0 0 0 0 | * * * * * * 12 * * * * * * * * | 0 0 1 0 0 1 1 0 0 0 | 2 0 1 xo3ox .. .. &#x || x.3o. .. .. & ♦ 9 | 9 0 6 3 6 | 3 0 0 6 0 3 0 6 0 6 | 0 0 1 0 0 1 0 0 1 0 0 0 3 3 0 0 0 | * * * * * * * 24 * * * * * * * | 0 0 0 1 1 0 0 1 0 0 | 1 2 0 xo .. xx .. &#x || x. .. o. .. & ♦ 8 | 3 3 4 4 4 | 0 1 0 2 2 2 2 2 2 4 | 0 0 0 1 0 0 1 0 0 0 1 0 2 0 2 0 0 | * * * * * * * * 36 * * * * * * | 0 0 0 1 0 1 0 0 1 0 | 1 1 1 xo .. .. oo &#x || x. .. .. x. & ♦ 7 | 3 2 2 4 4 | 0 1 0 1 0 2 2 2 2 4 | 0 0 0 0 0 0 1 0 0 1 0 0 2 0 0 2 0 | * * * * * * * * * 36 * * * * * | 0 0 0 0 1 1 0 0 1 0 | 1 1 1 .. ox xx .. &#x || .. o. o. .. & ♦ 7 | 2 3 4 2 4 | 0 1 0 2 2 0 1 2 2 4 | 0 0 0 1 0 0 0 0 0 1 0 0 0 2 2 0 0 | * * * * * * * * * * 36 * * * * | 0 0 0 1 0 0 1 0 1 0 | 1 1 1 .. ox .. oo &#x || .. o. .. x. & ♦ 5 | 1 1 2 2 4 | 0 0 0 1 0 0 1 2 2 4 | 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 2 0 | * * * * * * * * * * * 36 * * * | 0 0 0 0 1 0 1 0 1 0 | 1 1 1 .. .. xx3oo &#x || .. .. o.3x. & ♦ 9 | 0 9 3 6 6 | 0 0 3 0 3 0 6 0 6 6 | 0 0 0 0 1 0 0 1 0 0 0 1 0 0 3 3 0 | * * * * * * * * * * * * 24 * * | 0 0 0 0 0 1 1 0 0 1 | 1 0 2 xo .. .. .. &#x || xo .. .. .. &#x & ♦ 6 | 2 0 4 3 4 | 0 0 0 2 0 1 0 2 0 8 | 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 | * * * * * * * * * * * * * 36 * | 0 0 0 0 0 0 0 1 2 0 | 0 2 1 .. .. xx .. &#x || .. .. oo .. &#x & ♦ 6 | 0 2 3 4 4 | 0 0 0 0 1 0 2 0 2 8 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * * * * * * * 36 | 0 0 0 0 0 0 0 0 2 1 | 0 1 2 ------------------------------------+----+----------------+--------------------------------+--------------------------------------------------+-------------------------------------------+--------------------------+------ xo3ox xx3oo &#x .. .. .. .. & ♦ 18 | 18 18 18 0 0 | 6 18 6 18 18 0 0 0 0 0 | 6 6 3 18 6 0 0 0 0 0 0 0 0 0 0 0 0 | 2 3 6 0 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * | 2 0 0 x.3o. x.3o. || x.3o. o.3x. & ♦ 18 | 18 18 0 18 0 | 6 18 6 0 0 18 18 0 0 0 | 6 6 0 0 0 6 18 3 0 0 0 0 0 0 0 0 0 | 2 0 0 6 3 0 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * | 2 0 0 x.3o. x.3o. || .o3.x .o3.x & ♦ 18 | 18 18 0 0 36 | 6 18 6 0 0 0 0 36 36 0 | 6 6 0 0 0 0 0 0 6 18 18 6 0 0 0 0 0 | 2 0 0 0 0 6 6 0 0 0 0 0 0 0 0 | * * 2 * * * * * * * | 2 0 0 xo3ox xx .. &#x || x.3o. o. .. & ♦ 15 | 15 6 12 6 12 | 5 6 0 12 6 6 3 12 6 12 | 2 0 2 6 0 2 3 0 2 3 3 0 6 6 6 0 0 | 0 1 0 1 0 1 0 2 3 0 3 0 0 0 0 | * * * 12 * * * * * * | 1 1 0 xo3ox .. oo &#x || x.3o. .. x. & ♦ 12 | 12 3 6 6 12 | 4 3 0 6 0 6 3 12 6 12 | 1 0 1 0 0 2 3 0 2 3 3 0 6 6 0 6 0 | 0 0 0 1 0 1 0 2 0 3 0 3 0 0 0 | * * * * 12 * * * * * | 1 1 0 xo .. xx3oo &#x || x. .. o.3x. & ♦ 15 | 6 15 6 12 12 | 0 6 5 3 6 6 12 6 12 12 | 0 2 0 3 2 0 6 2 0 3 3 2 6 0 6 6 0 | 0 0 1 0 1 0 1 0 3 3 0 0 2 0 0 | * * * * * 12 * * * * | 1 0 1 .. ox xx3oo &#x || .. o. o.3x. & ♦ 12 | 3 12 6 6 12 | 0 3 4 3 6 0 6 6 12 12 | 0 1 0 3 2 0 0 1 0 3 3 2 0 6 6 6 0 | 0 0 1 0 0 0 1 0 0 0 3 3 2 0 0 | * * * * * * 12 * * * | 1 0 1 xo3ox .. .. &#x || xo3ox .. .. &#x ♦ 12 | 12 0 12 6 12 | 4 0 0 12 0 6 0 12 0 24 | 0 0 2 0 0 2 0 0 2 0 0 0 12 12 0 0 6 | 0 0 0 0 0 0 0 4 0 0 0 0 0 6 0 | * * * * * * * 6 * * | 0 2 0 xo .. xx .. &#x || xo .. oo .. &#x & ♦ 9 | 3 3 6 6 8 | 0 1 0 3 2 2 3 4 4 16 | 0 0 0 1 0 0 1 0 0 1 1 0 4 4 4 4 4 | 0 0 0 0 0 0 0 0 1 1 1 1 0 2 2 | * * * * * * * * 36 * | 0 1 1 .. .. xx3oo &#x || .. .. oo3xx &#x ♦ 12 | 0 12 6 12 12 | 0 0 4 0 6 0 12 0 12 24 | 0 0 0 0 2 0 0 2 0 0 0 2 0 0 12 12 6 | 0 0 0 0 0 0 0 0 0 0 0 0 4 0 6 | * * * * * * * * * 6 | 0 0 2 ------------------------------------+----+----------------+--------------------------------+--------------------------------------------------+-------------------------------------------+--------------------------+------ xo3ox xx3oo &#x || x.3o. o.3x. & ♦ 27 | 27 27 18 18 36 | 9 27 9 18 18 18 18 36 36 36 | 9 9 3 18 6 6 18 3 6 18 18 6 18 18 18 18 0 | 3 3 6 6 3 6 6 6 9 9 9 9 6 0 0 | 1 1 1 3 3 3 3 0 0 0 | 4 * * xo3ox xx .. &#x || xo3ox oo .. &#x & ♦ 18 | 18 6 18 12 24 | 6 6 0 18 6 12 6 24 12 48 | 2 0 3 6 0 4 6 0 4 6 6 0 24 24 12 12 12 | 0 1 0 2 0 2 0 8 6 6 6 6 0 12 6 | 0 0 0 2 2 0 0 2 6 0 | * 6 * xo .. xx3oo &#x || xo .. oo3xx &#x & ♦ 18 | 6 18 12 18 24 | 0 6 6 6 12 6 18 12 24 48 | 0 2 0 6 4 0 6 3 0 6 6 4 12 12 24 24 12 | 0 0 2 0 1 0 2 0 6 6 6 6 8 6 12 | 0 0 0 0 0 2 2 0 6 2 | * * 6
or o.3o. o.3o. .. .. .. .. & | 36 | 4 4 4 | 2 4 6 8 12 12 | 4 2 12 4 4 5 4 20 16 4 | 1 4 6 6 12 8 14 5 12 | 2 1 10 8 4 9 | 3 6 ------------------------------------+----+----------+---------------------+---------------------------------+---------------------------+-----------------+----- x. .. .. .. .. .. .. .. & | 2 | 72 * * | 1 2 1 2 2 0 | 3 1 5 2 2 2 1 4 2 0 | 1 2 4 4 6 3 5 1 2 | 2 1 7 5 2 3 | 3 4 oo3oo oo3oo &#x .. .. .. .. & | 2 | * 72 * | 0 0 2 2 0 4 | 0 1 4 1 0 0 0 8 6 2 | 0 2 2 0 6 4 6 2 7 | 1 0 6 4 3 6 | 2 5 o.3o. o.3o. || .o3.o .o3.o & | 2 | * * 72 | 0 0 0 0 4 2 | 0 0 0 0 2 2 2 4 4 1 | 0 0 0 4 4 2 4 2 4 | 0 1 4 4 2 4 | 2 4 ------------------------------------+----+----------+---------------------+---------------------------------+---------------------------+-----------------+----- x.3o. .. .. .. .. .. .. & | 3 | 3 0 0 | 24 * * * * * | 2 1 0 2 2 0 0 0 0 0 | 1 2 2 2 0 0 0 0 0 | 2 1 5 4 2 0 | 3 3 x. .. x. .. .. .. .. .. & | 4 | 4 0 0 | * 36 * * * * | 2 0 2 0 0 1 0 0 0 0 | 1 2 2 2 0 1 2 0 0 | 2 1 4 2 0 1 | 3 2 xo .. .. .. &#x .. .. .. .. & | 3 | 1 2 0 | * * 72 * * * | 0 1 2 0 0 0 0 2 2 0 | 0 2 1 0 4 2 3 1 2 | 1 0 5 3 2 3 | 2 4 .. .. xx .. &#x .. .. .. .. & | 4 | 2 2 0 | * * * 72 * * | 0 0 2 1 0 0 0 2 0 0 | 0 1 2 0 2 2 2 0 1 | 1 0 4 2 1 2 | 2 3 x. .. .. .. || .o .. .. .. & | 3 | 1 0 2 | * * * * 144 * | 0 0 0 0 1 1 1 1 1 0 | 0 0 0 3 2 1 2 1 1 | 0 1 3 3 1 2 | 2 3 oo3oo oo3oo &#x || o.3o. o.3o. & | 3 | 0 2 1 | * * * * * 144 | 0 0 0 0 0 0 0 2 2 1 | 0 0 0 0 2 1 2 1 4 | 0 0 2 2 2 4 | 1 4 ------------------------------------+----+----------+---------------------+---------------------------------+---------------------------+-----------------+----- x.3o. x. .. .. .. .. .. & ♦ 6 | 9 0 0 | 2 3 0 0 0 0 | 24 * * * * * * * * * | 1 1 1 1 0 0 0 0 0 | 2 1 2 1 0 0 | 3 1 xo3ox .. .. &#x .. .. .. .. & ♦ 6 | 6 6 0 | 2 0 6 0 0 0 | * 12 * * * * * * * * | 0 2 0 0 4 0 0 0 0 | 1 0 4 2 2 0 | 2 3 xo .. xx .. &#x .. .. .. .. & ♦ 6 | 5 4 0 | 0 1 2 2 0 0 | * * 72 * * * * * * * | 0 1 1 0 0 1 1 0 0 | 1 0 3 1 0 1 | 2 2 .. .. xx3oo &#x .. .. .. .. & ♦ 6 | 6 3 0 | 2 0 0 3 0 0 | * * * 24 * * * * * * | 0 0 2 0 2 0 0 0 0 | 1 0 2 2 1 0 | 2 2 x.3o. .. .. || .o3.x .. .. & ♦ 6 | 6 0 6 | 2 0 0 0 6 0 | * * * * 24 * * * * * | 0 0 0 2 2 0 0 0 0 | 0 1 2 2 1 0 | 2 2 x. .. x. .. || .o .. .o .. & ♦ 5 | 4 0 4 | 0 1 0 0 4 0 | * * * * * 36 * * * * | 0 0 0 2 0 0 2 0 0 | 0 1 2 2 0 1 | 2 2 x. .. .. o. || .o .. .. .x & ♦ 4 | 2 0 4 | 0 0 0 0 4 0 | * * * * * * 36 * * * | 0 0 0 2 0 1 0 1 0 | 0 1 2 2 0 1 | 2 2 xo .. .. .. &#x || x. .. .. .. & ♦ 5 | 2 4 2 | 0 0 1 1 1 2 | * * * * * * * 144 * * | 0 0 0 0 1 1 1 0 1 | 0 0 2 1 1 2 | 1 3 .. ox .. .. &#x || .. o. .. .. & ♦ 4 | 1 3 2 | 0 0 1 0 1 2 | * * * * * * * * 144 * | 0 0 0 0 1 0 1 1 1 | 0 0 1 2 1 2 | 1 3 oo3oo oo3oo &#x || oo3oo oo3oo &#x ♦ 4 | 0 4 2 | 0 0 0 0 0 4 | * * * * * * * * * 36 | 0 0 0 0 0 0 0 0 4 | 0 0 0 0 2 4 | 0 4 ------------------------------------+----+----------+---------------------+---------------------------------+---------------------------+-----------------+----- x.3o. x.3o. .. .. .. .. & ♦ 9 | 18 0 0 | 6 9 0 0 0 0 | 6 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * | 2 1 0 0 0 0 | 3 0 xo3ox xx .. &#x .. .. .. .. & ♦ 12 | 12 12 0 | 4 6 12 6 0 0 | 2 2 6 0 0 0 0 0 0 0 | * 12 * * * * * * * | 1 0 2 0 0 0 | 2 1 xo .. xx3oo &#x .. .. .. .. & ♦ 9 | 12 6 0 | 3 3 3 6 0 0 | 1 0 3 2 0 0 0 0 0 0 | * * 24 * * * * * * | 1 0 1 1 0 0 | 2 1 x.3o. x. .. || .o3.x .o .. & ♦ 9 | 12 0 12 | 3 3 0 0 18 0 | 1 0 0 0 2 3 3 0 0 0 | * * * 24 * * * * * | 0 1 1 1 0 0 | 2 1 xo3ox .. .. &#x || x.3o. .. .. & ♦ 9 | 9 9 6 | 3 0 6 3 6 6 | 0 1 0 1 1 0 0 3 3 0 | * * * * 48 * * * * | 0 0 1 1 1 0 | 1 2 xo .. xx .. &#x || x. .. o. .. & ♦ 8 | 6 8 4 | 0 1 4 4 4 4 | 0 0 2 0 0 0 1 4 0 0 | * * * * * 36 * * * | 0 0 2 0 0 1 | 1 2 xo .. .. oo &#x || x. .. .. x. & ♦ 7 | 5 6 4 | 0 1 3 2 4 4 | 0 0 1 0 0 1 0 2 2 0 | * * * * * * 72 * * | 0 0 1 1 0 1 | 1 2 .. ox .. oo &#x || .. o. .. x. & ♦ 5 | 2 4 4 | 0 0 2 0 4 4 | 0 0 0 0 0 0 1 0 4 0 | * * * * * * * 36 * | 0 0 0 2 0 1 | 1 2 xo .. .. .. &#x || xo .. .. .. &#x & ♦ 6 | 2 7 4 | 0 0 2 1 2 8 | 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * 72 | 0 0 0 0 1 2 | 0 3 ------------------------------------+----+----------+---------------------+---------------------------------+---------------------------+-----------------+----- xo3ox xx3oo &#x .. .. .. .. & ♦ 18 | 36 18 0 | 12 18 18 18 0 0 | 12 3 18 6 0 0 0 0 0 0 | 2 3 6 0 0 0 0 0 0 | 4 * * * * * | 2 0 x.3o. x.3o. || .o3.x .o3.x & ♦ 18 | 36 0 36 | 12 18 0 0 72 0 | 12 0 0 0 12 18 18 0 0 0 | 2 0 0 12 0 0 0 0 0 | * 2 * * * * | 2 0 xo3ox xx .. &#x || x.3o. o. .. & ♦ 15 | 21 18 12 | 5 6 15 12 18 12 | 2 2 9 2 2 3 3 12 6 0 | 0 1 1 1 2 3 3 0 0 | * * 24 * * * | 1 1 xo3ox .. oo &#x || x.3o. .. x. & ♦ 12 | 15 12 12 | 4 3 9 6 18 12 | 1 1 3 2 2 3 3 6 12 0 | 0 0 1 1 2 0 3 3 0 | * * * 24 * * | 1 1 xo3ox .. .. &#x || xo3ox .. .. &#x & ♦ 12 | 12 18 12 | 4 0 12 6 12 24 | 0 2 0 2 2 0 0 12 12 6 | 0 0 0 0 4 0 0 0 6 | * * * * 12 * | 0 2 xo .. xx .. &#x || xo .. oo .. &#x & ♦ 9 | 6 12 8 | 0 1 6 4 8 16 | 0 0 2 0 0 1 1 8 8 4 | 0 0 0 0 0 1 2 1 4 | * * * * * 36 | 0 2 ------------------------------------+----+----------+---------------------+---------------------------------+---------------------------+-----------------+----- xo3ox xx3oo &#x || x.3o. o.3x. & ♦ 27 | 54 36 36 | 18 27 36 36 72 36 | 18 6 36 12 12 18 18 36 36 0 | 3 6 12 12 12 9 18 9 0 | 2 1 6 6 0 0 | 4 * xo3ox xx .. &#x || xo3ox oo .. &#x & ♦ 18 | 24 30 24 | 6 6 24 18 36 48 | 2 3 12 4 4 6 6 36 36 12 | 0 1 2 2 8 6 12 6 18 | 0 0 2 2 2 6 | * 12
xoxo3oxox xxoo3ooxx&#x → height(1,2) = height(1,3) = height(2,4) = height(3,4) = sqrt(2/3) = 0.816497 = height of oct
height(1,4) = height(2,3) = 1/sqrt(3) = 0.577350 = height of tridafup
o...3o... o...3o... & | 36 | 4 4 4 | 2 4 6 8 12 12 | 4 2 12 4 4 5 4 20 16 4 | 1 4 6 6 12 8 14 5 12 | 2 1 10 8 4 9 | 3 6
-------------------------+----+----------+---------------------+---------------------------------+---------------------------+-----------------+-----
x... .... .... .... & | 2 | 72 * * | 1 2 1 2 2 0 | 3 1 5 2 2 2 1 4 2 0 | 1 2 4 4 6 3 5 1 2 | 2 1 7 5 2 3 | 3 4
oo..3oo.. oo..3oo..&#x & | 2 | * 72 * | 0 0 2 2 0 4 | 0 1 4 1 0 0 0 8 6 2 | 0 2 2 0 6 4 6 2 7 | 1 0 6 4 3 6 | 2 5
o..o3o..o o..o3o..o&#x & | 2 | * * 72 | 0 0 0 0 4 2 | 0 0 0 0 2 2 2 4 4 1 | 0 0 0 4 4 2 4 2 4 | 0 1 4 4 2 4 | 2 4
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x...3o... .... .... & | 3 | 3 0 0 | 24 * * * * * | 2 1 0 2 2 0 0 0 0 0 | 1 2 2 2 0 0 0 0 0 | 2 1 5 4 2 0 | 3 3
x... .... x... .... & | 4 | 4 0 0 | * 36 * * * * | 2 0 2 0 0 1 0 0 0 0 | 1 2 2 2 0 1 2 0 0 | 2 1 4 2 0 1 | 3 2
xo.. .... .... ....&#x & | 3 | 1 2 0 | * * 72 * * * | 0 1 2 0 0 0 0 2 2 0 | 0 2 1 0 4 2 3 1 2 | 1 0 5 3 2 3 | 2 4
.... .... xx.. ....&#x & | 4 | 2 2 0 | * * * 72 * * | 0 0 2 1 0 0 0 2 0 0 | 0 1 2 0 2 2 2 0 1 | 1 0 4 2 1 2 | 2 3
x..o .... .... ....&#x & | 3 | 1 0 2 | * * * * 144 * | 0 0 0 0 1 1 1 1 1 0 | 0 0 0 3 2 1 2 1 1 | 0 1 3 3 1 2 | 2 3
ooo.3ooo. ooo.3ooo.&#x & | 3 | 0 2 1 | * * * * * 144 | 0 0 0 0 0 0 0 2 2 1 | 0 0 0 0 2 1 2 1 4 | 0 0 2 2 2 4 | 1 4
-------------------------+----+----------+---------------------+---------------------------------+---------------------------+-----------------+-----
x...3o... x... .... & ♦ 6 | 9 0 0 | 2 3 0 0 0 0 | 24 * * * * * * * * * | 1 1 1 1 0 0 0 0 0 | 2 1 2 1 0 0 | 3 1
xo..3ox.. .... ....&#x & ♦ 6 | 6 6 0 | 2 0 6 0 0 0 | * 12 * * * * * * * * | 0 2 0 0 4 0 0 0 0 | 1 0 4 2 2 0 | 2 3
xo.. .... xx.. ....&#x & ♦ 6 | 5 4 0 | 0 1 2 2 0 0 | * * 72 * * * * * * * | 0 1 1 0 0 1 1 0 0 | 1 0 3 1 0 1 | 2 2
.... .... xx..3oo..&#x & ♦ 6 | 6 3 0 | 2 0 0 3 0 0 | * * * 24 * * * * * * | 0 0 2 0 2 0 0 0 0 | 1 0 2 2 1 0 | 2 2
x..o3o..x .... ....&#x & ♦ 6 | 6 0 6 | 2 0 0 0 6 0 | * * * * 24 * * * * * | 0 0 0 2 2 0 0 0 0 | 0 1 2 2 1 0 | 2 2
x..o .... x..o ....&#x & ♦ 5 | 4 0 4 | 0 1 0 0 4 0 | * * * * * 36 * * * * | 0 0 0 2 0 0 2 0 0 | 0 1 2 2 0 1 | 2 2
x..o .... .... o..x&#x & ♦ 4 | 2 0 4 | 0 0 0 0 4 0 | * * * * * * 36 * * * | 0 0 0 2 0 1 0 1 0 | 0 1 2 2 0 1 | 2 2
xox. .... .... ....&#x & ♦ 5 | 2 4 2 | 0 0 1 1 1 2 | * * * * * * * 144 * * | 0 0 0 0 1 1 1 0 1 | 0 0 2 1 1 2 | 1 3
.... oxo. .... ....&#x & ♦ 4 | 1 3 2 | 0 0 1 0 1 2 | * * * * * * * * 144 * | 0 0 0 0 1 0 1 1 1 | 0 0 1 2 1 2 | 1 3
oooo3oooo oooo3oooo&#x ♦ 4 | 0 4 2 | 0 0 0 0 0 4 | * * * * * * * * * 36 | 0 0 0 0 0 0 0 0 4 | 0 0 0 0 2 4 | 0 4
-------------------------+----+----------+---------------------+---------------------------------+---------------------------+-----------------+-----
x...3o... x...3o... & ♦ 9 | 18 0 0 | 6 9 0 0 0 0 | 6 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * | 2 1 0 0 0 0 | 3 0
xo..3ox.. xx.. ....&#x & ♦ 12 | 12 12 0 | 4 6 12 6 0 0 | 2 2 6 0 0 0 0 0 0 0 | * 12 * * * * * * * | 1 0 2 0 0 0 | 2 1
xo.. .... xx..3oo..&#x & ♦ 9 | 12 6 0 | 3 3 3 6 0 0 | 1 0 3 2 0 0 0 0 0 0 | * * 24 * * * * * * | 1 0 1 1 0 0 | 2 1
x..o3o..x x..o ....&#x & ♦ 9 | 12 0 12 | 3 3 0 0 18 0 | 1 0 0 0 2 3 3 0 0 0 | * * * 24 * * * * * | 0 1 1 1 0 0 | 2 1
xox.3oxo. .... ....&#x & ♦ 9 | 9 9 6 | 3 0 6 3 6 6 | 0 1 0 1 1 0 0 3 3 0 | * * * * 48 * * * * | 0 0 1 1 1 0 | 1 2
xox. .... xxo. ....&#x & ♦ 8 | 6 8 4 | 0 1 4 4 4 4 | 0 0 2 0 0 0 1 4 0 0 | * * * * * 36 * * * | 0 0 2 0 0 1 | 1 2
xox. .... .... oox.&#x & ♦ 7 | 5 6 4 | 0 1 3 2 4 4 | 0 0 1 0 0 1 0 2 2 0 | * * * * * * 72 * * | 0 0 1 1 0 1 | 1 2
.... oxo. .... oox.&#x & ♦ 5 | 2 4 4 | 0 0 2 0 4 4 | 0 0 0 0 0 0 1 0 4 0 | * * * * * * * 36 * | 0 0 0 2 0 1 | 1 2
xoxo .... .... ....&#x & ♦ 6 | 2 7 4 | 0 0 2 1 2 8 | 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * 72 | 0 0 0 0 1 2 | 0 3
-------------------------+----+----------+---------------------+---------------------------------+---------------------------+-----------------+-----
xo..3ox.. xx..3oo..&#x & ♦ 18 | 36 18 0 | 12 18 18 18 0 0 | 12 3 18 6 0 0 0 0 0 0 | 2 3 6 0 0 0 0 0 0 | 4 * * * * * | 2 0
x..o3o..x x..o3o..x&#x & ♦ 18 | 36 0 36 | 12 18 0 0 72 0 | 12 0 0 0 12 18 18 0 0 0 | 2 0 0 12 0 0 0 0 0 | * 2 * * * * | 2 0
xox.3oxo. xxo. ....&#x & ♦ 15 | 21 18 12 | 5 6 15 12 18 12 | 2 2 9 2 2 3 3 12 6 0 | 0 1 1 1 2 3 3 0 0 | * * 24 * * * | 1 1
xox.3oxo. .... oox.&#x & ♦ 12 | 15 12 12 | 4 3 9 6 18 12 | 1 1 3 2 2 3 3 6 12 0 | 0 0 1 1 2 0 3 3 0 | * * * 24 * * | 1 1
xoxo3oxox .... ....&#x & ♦ 12 | 12 18 12 | 4 0 12 6 12 24 | 0 2 0 2 2 0 0 12 12 6 | 0 0 0 0 4 0 0 0 6 | * * * * 12 * | 0 2
xoxo .... xxoo ....&#x & ♦ 9 | 6 12 8 | 0 1 6 4 8 16 | 0 0 2 0 0 1 1 8 8 4 | 0 0 0 0 0 1 2 1 4 | * * * * * 36 | 0 2
-------------------------+----+----------+---------------------+---------------------------------+---------------------------+-----------------+-----
xox.3oxo. xxo.3oox.&#x & ♦ 27 | 54 36 36 | 18 27 36 36 72 36 | 18 6 36 12 12 18 18 36 36 0 | 3 6 12 12 12 9 18 9 0 | 2 1 6 6 0 0 | 4 *
xoxo3oxox xxoo ....&#x & ♦ 18 | 24 30 24 | 6 6 24 18 36 48 | 2 3 12 4 4 6 6 36 36 12 | 0 1 2 2 8 6 12 6 18 | 0 0 2 2 2 6 | * 12
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