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)
  • on equator at {3} between tet and tet:   arccos(-7/8) = 151.044976°
  • else at {3} between tet and tet:   arccos(1/4) = 75.522488°
Confer
related CRFs:
etedpy  
general polytopal classes:
tetrahedrochora   Blind polytopes   bistratic lace towers  

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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