A tetrahedral ring is a term given in this work to a set of 
regular tetrahedra
joined face-to-face sharing a common edge (with internal conjoined faces removed).
These solids are deltahedra. The following table
summarizes names for specific values of 
.
 | polyhedron |
| 1 | regular tetrahedron |
| 2 | equilateral tetrahedral dipyramid |
| 3 | tritetrahedron |
Tetrahedral rings are deltahedra.
The 
cases provides a refutation of an assertion of Aristotle that regular tetrahedra
fill space (Aristotle 1939, p. 319; Lagarias and Zong 2012). In actuality, there
is a small gap between the first and last member of this ring with angle
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
where
 |
(5)
|
is the dihedral angle of the regular tetrahedron.
While the angle 
does not appear to have a standard name in the literature, the term "Aristotle
gap" seems an apropos moniker for it.
