Definition:Dodecahedron/Regular
< Definition:Dodecahedron(Redirected from Definition:Regular Dodecahedron)
Jump to navigation
Jump to search
Definition
A regular dodecahedron is a dodecahedron whose $12$ faces are all congruent regular pentagons.
It has:
Also see
- Results about regular dodecahedra can be found here.
Historical Note
In The Elements, this object is referred to just as a dodecahedron.
In the words of Euclid:
- A dodecahedron is a solid figure contained by twelve equal, equilateral, and equiangular pentagons.
(The Elements: Book $\text{XI}$: Definition $28$)
According to the Pythagorean tradition, the regular dodecahedron was the symbol associated with the sphere of the fixed stars, and later with the quintessence of the medieval alchemists.
Linguistic Note
The word dodecahedron derives from the Classical Greek δωδεκάεδρόν:
- dodeca (δωδεκά), meaning twelve
- hedron (a form of ἕδρα), meaning base or seat.
The technically correct plural of dodecahedron is dodecahedra, but the word dodecahedrons can often be found.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $5$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $12$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $20$
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): dodecahedron
- 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): $12$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $20$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): dodecahedron (plural dodecahedra)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): dodecahedron (plural dodecahedra)
- 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): dodecahedron (dodecahedra)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Platonic solid: $\text {(iv)}$