Acronym | hexepe |
Name |
hexadecachoric pennene, hexadecachoron-pyramid pyramid-pyramid-pyramid, tetrahedron atop fully orthogonal hexadecachoron, 1/4-lune of diacosipentacontahexazetton |
Circumradius | 1/sqrt(2) = 0.707107 |
Face vector | 12, 62, 180, 321, 361, 252, 102, 20 |
Confer |
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Incidence matrix according to Dynkin symbol
xo3oo3oo ox3oo3oo4oo&#x → height = 1/sqrt(8) = 0.353553 (pyramid product of tet with hex) o.3o.3o. o.3o.3o.4o. | 4 * ♦ 3 8 0 | 3 24 24 0 | 1 24 72 32 0 | 8 72 96 16 0 | 24 96 48 1 | 32 48 3 | 16 3 .o3.o3.o .o3.o3.o4.o | * 8 ♦ 0 4 6 | 0 6 24 12 | 0 4 36 48 8 | 1 24 72 32 1 | 6 48 48 4 | 12 32 6 | 8 4 ------------------------+-----+---------+------------+-----------------+---------------+-------------+---------+----- x. .. .. .. .. .. .. | 2 0 | 6 * * ♦ 2 8 0 0 | 1 16 24 0 0 | 8 48 32 0 0 | 24 64 16 0 | 32 32 1 | 16 2 oo3oo3oo oo3oo3oo4oo&#x | 1 1 | * 32 * ♦ 0 3 6 0 | 0 3 16 12 0 | 1 18 36 8 0 | 6 36 24 1 | 12 24 3 | 8 3 .. .. .. .x .. .. .. | 0 2 | * * 24 ♦ 0 0 4 4 | 0 0 6 16 4 | 0 4 24 16 1 | 1 16 24 4 | 4 16 6 | 4 4 ------------------------+-----+---------+------------+-----------------+---------------+-------------+---------+----- x.3o. .. .. .. .. .. | 3 0 | 3 0 0 | 4 * * * ♦ 1 8 0 0 0 | 8 24 0 0 0 | 24 32 0 0 | 32 16 0 | 16 1 xo .. .. .. .. .. ..&#x | 2 1 | 1 2 0 | * 48 * * ♦ 0 2 6 0 0 | 1 12 12 0 0 | 6 24 24 0 | 12 16 1 | 8 2 .. .. .. ox .. .. ..&#x | 1 2 | 0 2 1 | * * 96 * ♦ 0 0 3 4 0 | 0 3 12 4 0 | 1 12 12 1 | 4 12 3 | 4 3 .. .. .. .x3.o .. .. | 0 3 | 0 0 3 | * * * 32 ♦ 0 0 0 4 2 | 0 0 6 8 1 | 0 4 12 4 | 1 8 6 | 2 4 ------------------------+-----+---------+------------+-----------------+---------------+-------------+---------+----- x.3o.3o. .. .. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 | 1 * * * * ♦ 8 0 0 0 0 | 24 0 0 0 | 32 0 0 | 16 0 xo3oo .. .. .. .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 | * 32 * * * ♦ 1 6 0 0 0 | 6 12 0 0 | 12 8 0 | 8 1 xo .. .. ox .. .. ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * * 144 * * ♦ 0 2 4 0 0 | 1 8 4 0 | 4 8 1 | 4 2 .. .. .. ox3oo .. ..&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 | * * * 128 * ♦ 0 0 3 2 0 | 0 3 6 1 | 1 6 3 | 2 3 .. .. .. .x3.o3.o .. ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * 16 ♦ 0 0 0 4 1 | 0 0 6 4 | 0 4 6 | 1 4 ------------------------+-----+---------+------------+-----------------+---------------+-------------+---------+----- xo3oo3oo .. .. .. ..&#x ♦ 4 1 | 6 4 0 | 4 6 0 0 | 1 4 0 0 0 | 8 * * * * ♦ 6 0 0 0 | 12 0 0 | 8 0 xo3oo .. ox .. .. ..&#x ♦ 3 2 | 3 6 1 | 1 6 3 0 | 0 2 3 0 0 | * 96 * * * ♦ 1 4 0 0 | 4 4 0 | 4 1 xo .. .. ox3oo .. ..&#x ♦ 2 3 | 1 6 3 | 0 3 6 1 | 0 0 3 2 0 | * * 192 * * ♦ 0 2 2 0 | 1 4 1 | 2 2 .. .. .. ox3oo3oo ..&#x ♦ 1 4 | 0 4 6 | 0 0 6 4 | 0 0 0 4 1 | * * * 64 * ♦ 0 0 3 1 | 0 3 3 | 1 3 .. .. .. .x3.o3.o4.o ♦ 0 8 | 0 0 24 | 0 0 0 32 | 0 0 0 0 16 | * * * * 1 ♦ 0 0 0 4 | 0 0 6 | 0 4 ------------------------+-----+---------+------------+-----------------+---------------+-------------+---------+----- xo3oo3oo ox .. .. ..&#x ♦ 4 2 | 6 8 1 | 4 12 4 0 | 1 8 6 0 0 | 2 4 0 0 0 | 24 * * * | 4 0 0 | 4 0 xo3oo .. ox3oo .. ..&#x ♦ 3 3 | 3 9 3 | 1 9 9 1 | 0 3 9 3 0 | 0 3 3 0 0 | * 128 * * | 1 2 0 | 2 1 xo .. .. ox3oo3oo ..&#x ♦ 2 4 | 1 8 6 | 0 4 12 4 | 0 0 6 8 1 | 0 0 4 2 0 | * * 96 * | 0 2 1 | 1 2 .. .. .. ox3oo3oo4oo&#x ♦ 1 8 | 0 8 24 | 0 0 24 32 | 0 0 0 32 16 | 0 0 0 16 1 | * * * 4 | 0 0 3 | 0 3 ------------------------+-----+---------+------------+-----------------+---------------+-------------+---------+----- xo3oo3oo ox3oo .. ..&#x ♦ 4 3 | 6 12 3 | 4 18 12 1 | 1 12 18 4 0 | 3 12 6 0 0 | 3 4 0 0 | 32 * * | 2 0 xo3oo .. ox3oo3oo ..&#x ♦ 3 4 | 3 12 6 | 1 12 18 4 | 0 4 18 12 1 | 0 6 12 3 0 | 0 4 3 0 | * 64 * | 1 1 xo .. .. ox3oo3oo4oo&#x ♦ 2 8 | 1 16 24 | 0 8 48 32 | 0 0 24 64 16 | 0 0 32 32 1 | 0 0 16 2 | * * 6 | 0 2 ------------------------+-----+---------+------------+-----------------+---------------+-------------+---------+----- xo3oo3oo ox3oo3oo ..&#x ♦ 4 4 | 6 16 6 | 4 24 24 4 | 1 16 36 16 1 | 4 24 24 4 0 | 6 16 6 0 | 4 4 0 | 16 * xo3oo .. ox3oo3oo4oo&#x ♦ 3 8 | 3 24 24 | 1 24 72 32 | 0 8 72 96 16 | 0 24 96 48 1 | 0 32 48 3 | 0 16 3 | * 4
xo3oo3oo ox3oo3oo *e3oo&#x → height = 1/sqrt(8) = 0.353553 (pyramid product of tet with hex) o.3o.3o. o.3o.3o. *e3o. | 4 * ♦ 3 8 0 | 3 24 24 0 | 1 24 72 32 0 0 | 8 72 96 8 8 0 | 24 96 24 24 1 | 32 24 24 3 | 8 8 3 .o3.o3.o .o3.o3.o *e3.o | * 8 ♦ 0 4 6 | 0 6 24 12 | 0 4 36 48 4 4 | 1 24 72 16 16 1 | 6 48 24 24 4 | 12 16 16 6 | 4 4 4 ---------------------------+-----+---------+------------+------------------+------------------+----------------+------------+------ x. .. .. .. .. .. .. | 2 0 | 6 * * ♦ 2 8 0 0 | 1 16 24 0 0 0 | 8 48 32 0 0 0 | 24 64 8 8 0 | 32 16 16 1 | 8 8 2 oo3oo3oo oo3oo3oo *e3oo&#x | 1 1 | * 32 * ♦ 0 3 6 0 | 0 3 16 12 0 0 | 1 18 36 4 4 0 | 6 36 12 12 1 | 12 12 12 3 | 4 4 3 .. .. .. .x .. .. .. | 0 2 | * * 24 ♦ 0 0 4 4 | 0 0 6 16 2 2 | 0 4 24 8 8 1 | 1 16 12 12 4 | 4 8 8 6 | 2 2 4 ---------------------------+-----+---------+------------+------------------+------------------+----------------+------------+------ x.3o. .. .. .. .. .. | 3 0 | 3 0 0 | 4 * * * ♦ 1 8 0 0 0 0 | 8 24 0 0 0 0 | 24 32 0 0 0 | 32 8 8 0 | 8 8 1 xo .. .. .. .. .. ..&#x | 2 1 | 1 2 0 | * 48 * * ♦ 0 2 6 0 0 0 | 1 12 12 0 0 0 | 6 24 4 4 0 | 12 8 8 1 | 4 4 2 .. .. .. ox .. .. ..&#x | 1 2 | 0 2 1 | * * 96 * ♦ 0 0 3 4 0 0 | 0 3 12 2 2 0 | 1 12 6 6 1 | 4 6 6 3 | 2 2 3 .. .. .. .x3.o .. .. | 0 3 | 0 0 3 | * * * 32 ♦ 0 0 0 4 1 1 | 0 0 6 4 4 1 | 0 4 6 6 4 | 1 4 4 6 | 1 1 4 ---------------------------+-----+---------+------------+------------------+------------------+----------------+------------+------ x.3o.3o. .. .. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 | 1 * * * * * ♦ 8 0 0 0 0 0 | 24 0 0 0 0 | 32 0 0 0 | 4 4 0 xo3oo .. .. .. .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 | * 32 * * * * ♦ 1 6 0 0 0 0 | 6 12 0 0 0 | 12 4 4 0 | 4 4 1 xo .. .. ox .. .. ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * * 144 * * * ♦ 0 2 4 0 0 0 | 1 8 2 2 0 | 4 4 4 1 | 2 2 2 .. .. .. ox3oo .. ..&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 | * * * 128 * * ♦ 0 0 3 1 1 0 | 0 3 3 3 1 | 1 3 3 3 | 1 1 3 .. .. .. .x3.o3.o .. ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * 8 * ♦ 0 0 0 4 0 1 | 0 0 6 0 4 | 0 4 0 6 | 1 0 4 .. .. .. .x3.o .. *3.o ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * * 8 ♦ 0 0 0 0 4 1 | 0 0 0 6 4 | 0 0 4 6 | 0 1 4 ---------------------------+-----+---------+------------+------------------+------------------+----------------+------------+------ xo3oo3oo .. .. .. ..&#x ♦ 4 1 | 6 4 0 | 4 6 0 0 | 1 4 0 0 0 0 | 8 * * * * * ♦ 6 0 0 0 0 | 12 0 0 0 | 4 4 0 xo3oo .. ox .. .. ..&#x ♦ 3 2 | 3 6 1 | 1 6 3 0 | 0 2 3 0 0 0 | * 96 * * * * ♦ 1 4 0 0 0 | 4 2 2 0 | 2 2 1 xo .. .. ox3oo .. ..&#x ♦ 2 3 | 1 6 3 | 0 3 6 1 | 0 0 3 2 0 0 | * * 192 * * * ♦ 0 2 1 1 0 | 1 2 2 1 | 1 1 2 .. .. .. ox3oo3oo ..&#x ♦ 1 4 | 0 4 6 | 0 0 6 4 | 0 0 0 4 1 0 | * * * 32 * * ♦ 0 0 3 0 1 | 0 3 0 3 | 1 0 3 .. .. .. ox3oo .. *e3oo&#x ♦ 1 4 | 0 4 6 | 0 0 6 4 | 0 0 0 4 0 1 | * * * * 32 * ♦ 0 0 0 3 1 | 0 0 3 3 | 0 1 3 .. .. .. .x3.o3.o *3.o ♦ 0 8 | 0 0 24 | 0 0 0 32 | 0 0 0 0 8 8 | * * * * * 1 ♦ 0 0 0 0 4 | 0 0 0 6 | 0 0 4 ---------------------------+-----+---------+------------+------------------+------------------+----------------+------------+------ xo3oo3oo ox .. .. ..&#x ♦ 4 2 | 6 8 1 | 4 12 4 0 | 1 8 6 0 0 0 | 2 4 0 0 0 0 | 24 * * * * | 4 0 0 0 | 2 2 0 xo3oo .. ox3oo .. ..&#x ♦ 3 3 | 3 9 3 | 1 9 9 1 | 0 3 9 3 0 0 | 0 3 3 0 0 0 | * 128 * * * | 1 1 1 0 | 1 1 1 xo .. .. ox3oo3oo ..&#x ♦ 2 4 | 1 8 6 | 0 4 12 4 | 0 0 6 8 1 0 | 0 0 4 2 0 0 | * * 48 * * | 0 2 0 1 | 1 0 2 xo .. .. ox3oo .. *e3oo&#x ♦ 2 4 | 1 8 6 | 0 4 12 4 | 0 0 6 8 0 1 | 0 0 4 0 2 0 | * * * 48 * | 0 0 2 1 | 0 1 2 .. .. .. ox3oo3oo *e3oo&#x ♦ 1 8 | 0 8 24 | 0 0 24 32 | 0 0 0 32 8 8 | 0 0 0 8 8 1 | * * * * 4 | 0 0 0 3 | 0 0 3 ---------------------------+-----+---------+------------+------------------+------------------+----------------+------------+------ xo3oo3oo ox3oo .. ..&#x ♦ 4 3 | 6 12 3 | 4 18 12 1 | 1 12 18 4 0 0 | 3 12 6 0 0 0 | 3 4 0 0 0 | 32 * * * | 1 1 0 xo3oo .. ox3oo3oo ..&#x ♦ 3 4 | 3 12 6 | 1 12 18 4 | 0 4 18 12 1 0 | 0 6 12 3 0 0 | 0 4 3 0 0 | * 32 * * | 1 0 1 xo3oo .. ox3oo .. *e3oo&#x ♦ 3 4 | 3 12 6 | 1 12 18 4 | 0 4 18 12 0 1 | 0 6 12 0 3 0 | 0 4 0 3 0 | * * 32 * | 0 1 1 xo .. .. ox3oo3oo *e3oo&#x ♦ 2 8 | 1 16 24 | 0 8 48 32 | 0 0 24 64 8 8 | 0 0 32 16 16 1 | 0 0 8 8 2 | * * * 6 | 0 0 2 ---------------------------+-----+---------+------------+------------------+------------------+----------------+------------+------ xo3oo3oo ox3oo3oo ..&#x ♦ 4 4 | 6 16 6 | 4 24 24 4 | 1 16 36 16 1 0 | 4 24 24 4 0 0 | 6 16 6 0 0 | 4 4 0 0 | 8 * * xo3oo3oo ox3oo .. *e3oo&#x ♦ 4 4 | 6 16 6 | 4 24 24 4 | 1 16 36 16 0 1 | 4 24 24 0 4 0 | 6 16 0 6 0 | 4 0 4 0 | * 8 * xo3oo .. ox3oo3oo *e3oo&#x ♦ 3 8 | 3 24 24 | 1 24 72 32 | 0 8 72 96 8 8 | 0 24 96 24 24 1 | 0 32 24 24 3 | 0 8 8 3 | * * 4
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