Home page.

8-atom variant of the standard 12-atom Shashibo.
Version of Wednesday 26 January 2025.

It is essential to read the home page first. It describes the 12-atom version of the Shashibo, and this 8-atom page relies on it extensively. Importantly, the atom of the 8-atom version is the same as that of the 12-atom version.

§1. The 8-atom Shashibo differs qualitatively from the 12-atom, and is not simply a "33⅓% less" version. The 8-atom version has three primary shapes which play a role similar to that of the cube and rhodo of the 12-atom. However, with the 8-atom version the primary shapes do not stand in an inside-out relationship.

The primary shapes of the 8-atom are two dipyramids, named dip13 and dip24; and one tetrahedron, named tetr8 (pronounced "tetrate"); it is so named because it contains eight ordinary atoms, which are themselves tetrahedral. The two dips are congruent to each other, but the tetr8 is not geometrically similar to an atom.

The following images are polyhedral nets of the eight atoms, and are comparable to those of home page §5. Markings are similar to those on the home page.

these images are from group_8 in the download

Explanation
according to color of typography
In purple: The atoms are numbered 1 through 8. Otherwise, same as 12-atom version.
In red: Same as 12-atom version.
In green: Numbers 41 through 48 denote points that serve as a vertex of at least one primary shape.
In blue: Numbers 51 through 58 denote points that never serve as a vertex of a primary shape.
In brown: Same as 12-atom version.
In turquoise: Same as 12-atom version, indicating how faces meet in at least one primary shape.

§2. One dipyramid has vertices 41 and 43 as its apices; it is dip13, which is short for dipyramid-41-43. The other dipyramid has vertices 42 and 44 as its apices; it is dip24. They are congruent, each with an equator that is an isosceles triangle.

tetr8dip13 or dip24
The table below has three-dimensional Cartesian coordinates for the vertices of a tetr8, containing eight unit-size atoms and residing at a convenient location in space.

The vertices of the tetr8 are named E, F, G, and H.

The table below has three-dimensional Cartesian coordinates for the vertices of either dip, containing eight unit-size atoms and residing at a convenient location in space.

The apical vertices of the dips are named P and Q; the equatorial vertices are named R, S, and T.

E= (+1, 0,+½ )
F= (−1, 0,+½ )
G= (0, −1,−½ )
H= (0, +1,−½ )
P= (+½√2, 0,+½√2 )
Q= (+½√2, 0,−½√2 )
R= (0, +1,0 )
S= (0, −1,0 )
T= (+√2, 0,0 )
A two-letter name denotes a point midway between the indicated points. Although a midway point is not a vertex of the tetr8 or either dip, it is still a vertex of atoms therein.
EF= (0, 0,+½ )
GH= (0, 0,−½ )
EG= (+½, −½,0 )
FH= (−½, +½,0 )
EH= (+½, +½,0 )
FG= (−½, −½,0 )
RS= (0, 0,0 )
RT= (+½√2, +½,0 )
ST= (+½√2, −½,0 )

Atoms meeting at each point:

tetr8
E45
F47
G46
H48
EF41 43
GH42 44
EG53 54
FH57 58
EH51 52
FG55 56
dip13
P41
Q43
R48
S46
T45 47
RS42 44
RT51 52 57 58
ST53 54 55 56
dip24
P42
Q44
R47
S45
T46 48
RS41 43
RT55 56 57 58
ST51 52 53 54

With any of the three primary shapes, every atom vertex is exposed on an edge; none is internal.

Also with the primary shapes, the atoms forming diatoms 1-2, 3-4, 5-6, and 7-8 are never separated. However, with non-primary shapes these diatoms are sometimes split.

If the eight atoms are detached at their hinges, they can be arranged into a tetrahedron geometrically similar to a single atom. However, the present author has not found a way to do this if they all remain attached.

§3. Below are two axonometric views of each of the three primary shapes. The images of dip13 and dip24 are the same except for the names of atom faces. This is possible because the two dips are congruent, differing only in which atoms are placed where.

  these images are from group_8 in the download
tetr8
dip13
dip24

A gray line separates adjoining faces that are coplanar. A gray line is never the location of a hinge.