Acronym | tete (old: tedpy) |
Name |
(line-)tetrahedron-tegum, tetrahedral bipyramid |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles
(at margins) | |
Face vector | 6, 14, 16, 8 |
Confer |
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External links |
Note, that the vertex figure of the equatorial vertices here might look like being a tridpy, when considering their faces only. But vertex figures have always to be orbiform, and tridpy surely is not. In fact, those verfs are an object from 2 tets, being attached within 4D slightly folded.
Incidence matrix according to Dynkin symbol
oxo3ooo3ooo&#xt → both heights = sqrt(5/8) = 0.790569 (pt || pseudo tet || pt) o..3o..3o.. | 1 * * ♦ 4 0 0 | 6 0 0 | 4 0 .o.3.o.3.o. | * 4 * | 1 3 1 | 3 3 3 | 3 3 ..o3..o3..o | * * 1 ♦ 0 0 4 | 0 0 6 | 0 4 ---------------+-------+-------+-------+---- oo.3oo.3oo.&#x | 1 1 0 | 4 * * | 3 0 0 | 3 0 .x. ... ... | 0 2 0 | * 6 * | 1 2 1 | 2 2 .oo3.oo3.oo&#x | 0 1 1 | * * 4 | 0 0 3 | 0 3 ---------------+-------+-------+-------+---- ox. ... ...&#x | 1 2 0 | 2 1 0 | 6 * * | 2 0 .x.3.o. ... | 0 3 0 | 0 3 0 | * 4 * | 1 1 .xo ... ...&#x | 0 2 1 | 0 1 2 | * * 6 | 0 2 ---------------+-------+-------+-------+---- ox.3oo. ...&#x ♦ 1 3 0 | 3 3 0 | 3 1 0 | 4 * .xo3.oo ...&#x ♦ 0 3 1 | 0 3 3 | 0 1 3 | * 4
or o..3o..3o.. & | 2 * ♦ 4 0 | 6 0 | 4 .o.3.o.3.o. | * 4 | 2 3 | 6 3 | 6 ------------------+-----+-----+------+-- oo.3oo.3oo.&#x & | 1 1 | 8 * | 3 0 | 3 .x. ... ... | 0 2 | * 6 | 2 2 | 4 ------------------+-----+-----+------+-- ox. ... ...&#x & | 1 2 | 2 1 | 12 * | 2 .x.3.o. ... | 0 3 | 0 3 | * 4 | 2 ------------------+-----+-----+------+-- ox.3oo. ...&#x & ♦ 1 3 | 3 3 | 3 1 | 8
yo ox3oo3oo&#zx → height = 0 (y = sqrt(5/2) = 1.581139) (tegum product of line with tet) o. o.3o.3o. | 2 * ♦ 4 0 | 6 0 | 4 .o .o3.o3.o | * 4 | 2 3 | 6 3 | 6 ---------------+-----+-----+------+-- oo oo3oo3oo&#x | 1 1 | 8 * | 3 0 | 3 .. .x .. .. | 0 2 | * 6 | 2 2 | 4 ---------------+-----+-----+------+-- .. ox .. ..&#x | 1 2 | 2 1 | 12 * | 2 .. .x3.o .. | 0 3 | 0 3 | * 4 | 2 ---------------+-----+-----+------+-- .. ox3oo ..&#x ♦ 1 3 | 3 3 | 3 1 | 8
oyo ooo3oox&#xt → height(1,2) = sqrt(3/8) = 0.612372 height(2,3) = 1/sqrt(24) = 0.204124 y = sqrt(5/2) = 1.581139 o.. o..3o.. | 1 * * | 2 3 0 0 | 6 3 0 0 | 6 0 .o. .o.3.o. | * 2 * ♦ 1 0 3 0 | 3 0 3 0 | 3 1 ..o ..o3..o | * * 3 | 0 1 2 2 | 2 2 4 1 | 4 2 ---------------+-------+---------+---------+---- oo. oo.3oo.&#x | 1 1 0 | 2 * * * | 3 0 0 0 | 3 0 o.o o.o3o.o&#x | 1 0 1 | * 3 * * | 2 2 0 0 | 4 0 .oo .oo3.oo&#x | 0 1 1 | * * 6 * | 1 0 2 0 | 2 1 ... ... ..x | 0 0 2 | * * * 3 | 0 1 2 1 | 2 2 ---------------+-------+---------+---------+---- ooo ooo3ooo&#x | 1 1 1 | 1 1 1 0 | 6 * * * | 2 0 ... ... o.x&#x | 1 0 2 | 0 2 0 1 | * 3 * * | 2 0 ... ... .ox&#x | 0 1 2 | 0 0 2 1 | * * 6 * | 1 1 ... ..o3..x | 0 0 3 | 0 0 0 3 | * * * 1 | 0 2 ---------------+-------+---------+---------+---- ... ... oox&#x ♦ 1 1 2 | 1 2 2 1 | 2 1 1 0 | 6 * ... .oo3.ox&#x ♦ 0 1 3 | 0 0 3 3 | 0 0 3 1 | * 2
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