Definition:Tetrahedron/Regular
Definition
A regular tetrahedron is a tetrahedron whose $4$ faces are all congruent equilateral triangles.
It has:
The regular tetrahedron is an example of a deltahedron.
Also known as
It is commonplace for authors to refer to a regular tetrahedron as just a tetrahedron, glossing over the fact of its regularity.
Also see
- Results about regular tetrahedra can be found here.
Historical Note
The concept of a regular tetrahedron is not mentioned explicitly by Euclid in The Elements.
The first reference to it is in Proposition $13$ of Book $\text{XIII} $: Construction of Regular Tetrahedron within Given Sphere:
In the words of Euclid:
- To construct a pyramid, to comprehend it in a given sphere, and to prove that the square on the diameter of the sphere is one and a half times the square on the side of the pyramid.
(The Elements: Book $\text{XIII}$: Proposition $13$)
According to the Pythagorean tradition, the regular tetrahedron was the symbol for the element fire.
Linguistic Note
The word tetrahedron derives from the Classical Greek τετράεδρόν:
- tetrás (τετράς), meaning four
- hedron (a form of ἕδρα), meaning base or seat.
The technically correct plural of tetrahedron is tetrahedra, but the word tetrahedrons can often be found.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $5$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $6$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $8$
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): tetrahedron
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Platonic solid
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.4$: Euclid (flourished ca. $300$ B.C.)
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $8$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): tetrahedron (plural tetrahedra)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): tetrahedron (plural tetrahedra)
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $2$: The Logic of Shape: Euclid
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Platonic solid: $\text {(i)}$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): tetrahedron (tetrahedra)