- Truncated tetrahedron
The

**truncated tetrahedron**is anArchimedean solid . It has 4 regularhexagon al faces, 4 regular triangular faces, 12 vertices and 18 edges.**Area and volume**The area "A" and the

volume "V" of a truncated tetrahedron of edge length "a" are::$A\; =\; 7sqrt\{3\}a^2\; approx\; 12.1243557a^2$:$V\; =\; frac\{23\}\{12\}sqrt\{2\}a^3\; approx\; 2.71057599a^3.$**Cartesian coordinates**Cartesian coordinates for the 12 vertices of a truncatedtetrahedron centered at the origin, with edge length √8, are all permutations of (±1,±1,±3) with an even number of minus signs:

* (+3,+1,+1), (+1,+3,+1), (+1,+1,+3)

* (−3,−1,+1), (−1,−3,+1), (−1,−1,+3)

* (−3,+1,−1), (−1,+3,−1), (−1,+1,−3)

* (+3,−1,−1), (+1,−3,−1), (+1,−1,−3)**Use in architecture**Giant truncated tetrahedrons were used for the "Man the explorer" and "Man the producer" theme pavilions in

Expo 67 . They were made of massive girders of steel bolted together in a geometric lattice. The tetrahedrons were interconnected with lattice steel platforms. All of these buildings were demolished after the end of Expo 67, as they had not been built to withstand the severity of the Montreal weather over the years. Their only remnants are in the Montreal city archives, the Public Archives Of Canada and the photo collections of tourists of the times.**ee also***

octahedron

*tetrahedron **References*** (Section 3-9)

**External links***

* [*http://www.mathconsult.ch/showroom/unipoly/ The Uniform Polyhedra*]

* [*http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra*] The Encyclopedia of Polyhedra

* [*http://www.lifeisastoryproblem.org/explore/net_truncated_tetrahedron.pdf Printable Net of a Truncated Tetrahedron*] [*http://www.lifeisastoryproblem.org Life is a Story Problem.org*]

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