Definition:Octahedron/Regular
Jump to navigation
Jump to search
Definition
A regular octahedron is an octahedron whose $8$ faces are all congruent equilateral triangles.
It has:
The regular octahedron is an example of a deltahedron.
Also known as
It is commonplace for authors to refer to a regular octahedron as just an octahedron, glossing over the fact of its regularity.
Also see
- Results about regular octahedra can be found here.
Historical Note
Euclid in The Elements refers to this object just as an octahedron.
In the words of Euclid:
- An octahedron is a solid figure contained by eight equal and equilateral triangles.
(The Elements: Book $\text{XI}$: Definition $26$)
According to the Pythagorean tradition, the regular octahedron was the symbol for the element air.
Linguistic Note
The word octahedron derives from the Classical Greek:
- octo (ὀκτώ), meaning eight
- hedron (a form of ἕδρα), meaning base or seat.
The technically correct plural of octahedron is octahedra, but the word octahedrons can often be found.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $4$
- 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): octahedron
- 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): $4$
- 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): octahedron (plural octahedra)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): octahedron (plural octahedra)
- 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: $\text {(iii)}$