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In analogy with the cross-section of a solid, the cross-section of an n-dimensional body in an n-dimensional space is the non-empty intersection of the body with a hyperplane (an (n − 1)-dimensional subspace). This concept has sometimes been used to help visualize aspects of higher dimensional spaces. [7]
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. When one of these planes intersects the tetrahedron the resulting cross section is a rectangle. [11] When the intersecting plane is near one of the edges the rectangle is long and skinny.
The icosidodecahedron is an Archimedean solid, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces meet in a vertex. [5] The polygonal faces that meet for every vertex are two equilateral triangles and two regular pentagons, and the vertex figure of an icosidodecahedron is {{nowrap|(3 ...
The ten-of-diamonds can be dissected in an octagonal cross-section between the two rhombic faces. It is a decahedron with 12 vertices, 20 edges, and 10 faces (4 triangles, 4 trapezoids, 1 rhombus, and 1 isotoxal octagon). Michael Goldberg labels this polyhedron 10-XXV, the 25th in a list of space-filling decahedra. [2]
In geometry, an icosahedron (/ ˌ aɪ k ɒ s ə ˈ h iː d r ən,-k ə-,-k oʊ-/ or / aɪ ˌ k ɒ s ə ˈ h iː d r ən / [1]) is a polyhedron with 20 faces. The name comes from Ancient Greek εἴκοσι (eíkosi) 'twenty' and ἕδρα (hédra) 'seat'. The plural can be either "icosahedra" (/-d r ə /) or "icosahedrons".
The regular octahedron can be considered as the antiprism, a prism like polyhedron in which lateral faces are replaced by alternating equilateral triangles. It is also called trigonal antiprism. [21] Therefore, it has the property of quasiregular, a polyhedron in which two different polygonal faces are alternating and meet at a vertex. [22]
The diagonal of a matrix denotes the number of each element that appears in a polyhedron, whereas the non-diagonal of a matrix denotes the number of the column's elements that occur in or at the row's element. The rhombic dodecahedron has vertex classes with 8+6, 1 edge class of 24, and 1 face class of 12; each element in a matrix's diagonal.
Ten ten-sided dice. The pentagonal trapezohedron was patented for use as a gaming die (i.e. "game apparatus") in 1906. [1] These dice are used for role-playing games that use percentile-based skills; however, a twenty-sided die can be labeled with the numbers 0-9 twice to use for percentages instead.