Tetrahedron in a sentence

Cross section of regular tetrahedron A central cross section of a regular tetrahedron is a square The two skew perpendicular opposite edges of a regular tetrahedron define a set of parallel planes.

A line segment joining a vertex of a tetrahedron with the centroid of the opposite face is called a median and a line segment joining the midpoints of two opposite edges is called a bimedian of the tetrahedron.

Correspondingly, a regular octahedron is the result of cutting off from a regular tetrahedron, four regular tetrahedra of half the linear size (i.e. rectifying the tetrahedron).

However, there is generally no orthocenter in the sense of intersecting altitudes. citation Gaspard Monge found a center that exists in every tetrahedron, now known as the Monge point: the point where the six midplanes of a tetrahedron intersect.

Isometries of irregular tetrahedra The isometries of an irregular (unmarked) tetrahedron depend on the geometry of the tetrahedron, with 7 cases possible.

The symmetries of a regular tetrahedron correspond to those of a cube which map each tetrahedron to itself; the other symmetries of the cube map the two to each other.

The vertices of the octahedron lie at the midpoints of the edges of the tetrahedron, and in this sense it relates to the tetrahedron in the same way that the cuboctahedron and icosidodecahedron relate to the other Platonic solids.

Though the surface area of each subsequent tetrahedron is that of the tetrahedron in the previous iteration, there are 4 times as many—thus maintaining a constant total surface area.

The Onion’s make-believe owner, Bryce P. Tetraeder, Global Tetrahedron CEO, penned the explainer about why he chose to buy Jones’ reprehensible site.

One of the day’s activities on Feb. 8 will give the students a chance to build their own tetrahedron.

The scientists first derived equations to describe a quantum tetrahedron within a spin network.

All sp 3 -hybridized atoms are surrounded by atoms (or lone electron pairs ) at the four corners of a tetrahedron.

Also, in part due to self-duality of the tetrahedron, only one Archimedean solid has only tetrahedral symmetry.

A negative value of the determinant means that a tetrahedron cannot be constructed with the given distances.

A number of designs were used, including a tetrahedron which could be close-packed without waste space, and could not be knocked over accidentally.

A regular tetrahedron can be embedded inside a cube in two ways such that each vertex is a vertex of the cube, and each edge is a diagonal of one of the cube's faces.

Clearly the sum of the angles of any side of the tetrahedron must be 180°.

Continuing with our example, a tetrahedron has one 3-dimensional element (itself), four 2-dimensional elements (faces), six 1-dimensional elements (edges), and four 0-dimensional elements (vertices).

Earth was associated with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron.

Fire can be extinguished by removing any one of the elements of the fire tetrahedron.