One can take a regular tetrahedron, then cut halves-dimension-wise off it vertices with planar cuts. That's four different planes.
That produces 4 regular tetrahedrons half-gabarit, as well as a regular octahedron posing a kernel.
When such an octahedron gets taken, 6 vertices, and you cut halves dimension-wise off it likewise, in addition to 6 regular half-gabarit octahedrons you get 8 regular tetrahedrons adjoined. The cuts all add up magically to there being 4 cutting planes.
Both cases, cuts naturally go through midpoints of edges only.
Aforementioned octahedral kernel taken and cut half-gabarit, the cutting planes, 4 in quantity, are parallels to those having that octahedron produced out of tetrahedral starting.
Being continued onto the 4 half-gabarit tetrahedrons adjoining kernel they produce parts of half-gabarit cuts onto them similarily to how the tetrahedron starting ended eventually cut.
There is a regular tetrahedron. There are four faces of it. You take 4 packets of in-packet parallel planes, each packet parallel to its face tetrahedral.
These packets, intersecting in between of themselves produce tesselation of space consisting of regular tetrahedrons and regular octahedron if the in-packet step's everywhere constant, say a centimeter in between of the neighbouring in-packet planes.
This is a tesselation of space in two elements versus one, alternate to cubic tesselation, achieved in three packets.
Looks trig, as opposed to quad.
Disphenoid tetrahedral tesselation is derivative of the cubic having no relation to tetraoctahedral described.
Never mind.
That produces 4 regular tetrahedrons half-gabarit, as well as a regular octahedron posing a kernel.
When such an octahedron gets taken, 6 vertices, and you cut halves dimension-wise off it likewise, in addition to 6 regular half-gabarit octahedrons you get 8 regular tetrahedrons adjoined. The cuts all add up magically to there being 4 cutting planes.
Both cases, cuts naturally go through midpoints of edges only.
Aforementioned octahedral kernel taken and cut half-gabarit, the cutting planes, 4 in quantity, are parallels to those having that octahedron produced out of tetrahedral starting.
Being continued onto the 4 half-gabarit tetrahedrons adjoining kernel they produce parts of half-gabarit cuts onto them similarily to how the tetrahedron starting ended eventually cut.
There is a regular tetrahedron. There are four faces of it. You take 4 packets of in-packet parallel planes, each packet parallel to its face tetrahedral.
These packets, intersecting in between of themselves produce tesselation of space consisting of regular tetrahedrons and regular octahedron if the in-packet step's everywhere constant, say a centimeter in between of the neighbouring in-packet planes.
This is a tesselation of space in two elements versus one, alternate to cubic tesselation, achieved in three packets.
Looks trig, as opposed to quad.
Disphenoid tetrahedral tesselation is derivative of the cubic having no relation to tetraoctahedral described.
Never mind.
