Space diagonal information

a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals...

In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any...

In a magic cube, a broken space diagonal is a sequence of cells of the cube that follows a line parallel to a space diagonal of the cube, and continues...

glide along the half of a diagonal of a face, and the d glide, which is along a quarter of either a face or space diagonal of the unit cell. The d glide...

A=2(ab+ac+bc).} its space diagonal can be found by constructing a right triangle of height c {\displaystyle c} with its base as the diagonal of the a {\displaystyle...

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...

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices...

edge lengths are relatively prime. A perfect Euler brick is one whose space diagonal is also an integer, but such a brick has not yet been found. The definition...

Whereas a square of unit side length has a diagonal equal to 2 {\displaystyle {\sqrt {2}}} , a space diagonal inside a tesseract measures 2 when its side...

non-defective if it is similar to a diagonal matrix. That is, if there exists an invertible matrix P {\displaystyle P}  and a diagonal matrix D {\displaystyle D}...

Face diagonal: d 2 = 2 s {\displaystyle d_{\mathrm {2} }={\sqrt {2}}s} Cell diagonal: d 3 = 3 s {\displaystyle d_{\mathrm {3} }={\sqrt {3}}s} 4-space diagonal:...

downward along a space diagonal). On level 2: can move and capture one step diagonally; can move and capture to level 3, to a square diagonally adjacent to...

It has 12 faces, 20 vertices, 30 edges, and 160 diagonals (60 face diagonals, 100 space diagonals). It is represented by the Schläfli symbol {5,3}....

the half of a diagonal of a face, and the d {\displaystyle d} glide, which is a fourth of the way along either a face or space diagonal of the unit cell...

of a regular hexagon with sides of length 1. It is the length of the space diagonal of a unit cube. The vesica piscis has a major axis to minor axis ratio...

diagonal of the cube or any midline of the faces is a Cantor set. The cross-section of the sponge through its centroid and perpendicular to a space diagonal...

defines a cuboid with integer side lengths |a|, |b|, and |c|, whose space diagonal has integer length d; with this interpretation, Pythagorean quadruples...

squares of the edges of a rectangular cuboid equals the square of any space diagonal Sums of powers Sum of reciprocals Quadratic form (statistics) Reduced...

cube. The rows and columns correspond to vertices, edges, and faces. The diagonal numbers say how many of each element occur in the whole cube. The nondiagonal...

{\displaystyle a\,} is the other cathetus. Mathematics portal Cathetus Triangle Space diagonal Nonhypotenuse number Taxicab geometry Trigonometry Special right triangles...

rather than the centers of the faces. There are four axes, one for each space diagonal of the cube. As a result, it is a deep-cut puzzle in which each twist...

the direct sum of two vector spaces of matrices could be represented as a direct sum of two matrices. A block diagonal matrix is a block matrix that...

tangent functions respectively. OEIS: A195696 θm is the angle between the space diagonal of a cube and any of its three connecting edges, see image. Another...

{d^{2}+(r_{2}-r_{1})^{2}}}-r_{3}.} The spoke length formula computes the length of the space diagonal of an imaginary rectangular box. Imagine holding a wheel in front of...

(on upper board). 3D movement: Can move or capture one jump along a space diagonal below or above. Gryphon 1X.n+ t[FR] Grant Acedrex (Alfonso X, 1283)...

matrix, normal operator Orthogonal matrix Unitary matrix Semi-Hilbert space Diagonal matrix Eigenvector, eigenvalue, eigenfunction Hermitian operator self-adjoint...

corresponding diagonal matrix. The concept of diagonalization is relatively straightforward for operators on finite-dimensional vector spaces but requires...

Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of...