Elementary geometry

Face diagonal

In geometry, a face diagonal of a polyhedron is a diagonal on one of the faces, in contrast to a space diagonal passing through the interior of the polyhedron. A cuboid has twelve face diagonals (two on each of the six faces), and it has four space diagonals. The cuboid's face diagonals can have up to three different lengths, since the faces come in congruent pairs and the two diagonals on any face are equal. The cuboid's space diagonals all have the same length. If the edge lengths of a cuboid are a, b, and c, then the distinct rectangular faces have edges (a, b), (a, c), and (b, c); so the respective face diagonals have lengths and Thus each face diagonal of a cube with side length a is . A regular dodecahedron has 60 face diagonals (and 100 space diagonals). (Wikipedia).

Face diagonal
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From playlist The Diagonalization of Matrices

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Watch more videos on http://www.brightstorm.com/math/geometry SUBSCRIBE FOR All OUR VIDEOS! https://www.youtube.com/subscription_center?add_user=brightstorm2 VISIT BRIGHTSTORM.com FOR TONS OF VIDEO TUTORIALS AND OTHER FEATURES! http://www.brightstorm.com/ LET'S CONNECT! Facebook ► https

From playlist Geometry

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Every operator on a finite-dimensional complex vector space has a matrix (with respect to some basis of the vector space) that is a block diagonal matrix, with each block itself an upper-triangular matrix that contains only one eigenvalue on the diagonal.

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From playlist Introduction to Matrices and Matrix Operations

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Watch more videos on http://www.brightstorm.com/math/geometry SUBSCRIBE FOR All OUR VIDEOS! https://www.youtube.com/subscription_center?add_user=brightstorm2 VISIT BRIGHTSTORM.com FOR TONS OF VIDEO TUTORIALS AND OTHER FEATURES! http://www.brightstorm.com/ LET'S CONNECT! Facebook ► http

From playlist Geometry

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Related pages

Cube | Dodecahedron | Polyhedron | Geometry | Cuboid | Diagonal | Space diagonal