# Tetrahedron

Read here about the simplest poyhedron, the tetrahedron, a basic building block of the real world, hence an important concept in tensegrity structures. The tetrahedron is often deployed or described by tensegrity structures. See also octahedron, icosahedron, and the other polyhedra.

# Overview

A **tetrahedron** (plural: **tetrahedra**) in classic geometry is a [polyhedron] composed of four triangular faces, three of which meet at each [[http//en.wikipedia.org/wiki/Vertex_(geometry) vertex]. A **regular tetrahedron** is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids. The tetrahedron is the only convex polyhedron that has four faces. The tetrahedron is the three-dimensional case of the more general concept of a [[http

# Truncated Tetrahedron

The truncated tetrahedron has 18 edges, 8 faces and 12 vertexes. A tensegrity that outlines this polyhedron has 6 struts and 18 tensile vectors. It was first exhibited by Francesco della Sala at the University of Michigan in 1952, according to Burkhardt.

Motro calls such structures tensypolyhedra. He rendered the structure with 6 struts and 18 tensile vectors.

Tibert compares in the drawing below an idealized polyhedron drawn with dashed lines, and a tensegrity that outlines the polyhedron, drawn with black heavy struts and light black tension members. He renders a truncated tetrahedron.

Burkhardt classifies this model as a “zig-zag” tensegrity because each strut is supported by two other struts tied into a zig-zag of three tendons spanning the strut. The 6 strut tensegrity structure that conforms with the truncated tetrahedron is the zig-zag counterpart of the 6 strut icosahedron, as both structures have 6 struts. But this truncated tetrahedron-like model has four tendon triangles, whereas the icosahedron-like model has eight.

C. R. Calladine uses this tensegrity as the basis for his analysis of tensegrity structures in terms of Maxwell’s stiffness rule.

# Image Gallery of Tetrahedron-like Tensegrity Structures

Pars shared the image below:

Angelo shared the image below, showing a 4-struts, "real" tetrahedron (4 vertices, 6 edges, 4 equal triangular faces etc.- http://hardstudio.altervista.org/tensegrity-tetraedro.html):

http://hardstudio.altervista.org/tensegrity-tetraedro-files/bild14-small.jpg

This is a first attempt to generate tensegrities shaping the platonic solids - see a cube from the same author

Below Marcelo Pars version of a real tetrahedron. Probably the most simple tetrahedron possible, with only 4 struts and ten strings.

http://www.tensegriteit.nl/afbeelding/tensegrity217.jpg

The tetrahedron is also available on Marcelo Pars' 3D images Another variation of this perfect tetrahedron is a tensegrity with two bowed struts (each strut is half a circle):

http://www.tensegriteit.nl/afbeelding/tensegrity218.jpg

An ordinary tetrahedron on a fall day.

http://3.bp.blogspot.com/-w4uecDSorH8/U2I0Zbj1FUI/AAAAAAAACqM/8x3IBHUlXyw/s1600/trembling-tetra.jpg

See also Pars' tetrahedrons

# Online 3d Application Modeling The Tensegrity Tetrahedron

The tetrahedron, both ordinary and "Snelson" version, is available in the Xozzox online 3D simulation java application. In the object selection box on left, select "TetrahedronSnelson" or "Tetrahedron."