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  2. Truncated triangular pyramid number - Wikipedia

    en.wikipedia.org/wiki/Truncated_Triangular...

    A pyramid with side length 5 contains 35 spheres. Each layer represents one of the first five triangular numbers. A truncated triangular pyramid number [1] is found by removing some smaller tetrahedral number (or triangular pyramidal number) from each of the vertices of a bigger tetrahedral number.

  3. Snub disphenoid - Wikipedia

    en.wikipedia.org/wiki/Snub_disphenoid

    It is an example of deltahedron and Johnson solid. It can be constructed in different approaches. This shape is also called Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron. The snub disphenoid can be visualized as an atom cluster surrounding a central atom, that is the dodecahedral molecular geometry.

  4. Pyramidal number - Wikipedia

    en.wikipedia.org/wiki/Pyramidal_number

    The term often refers to square pyramidal numbers, which have a square base with four sides, but it can also refer to a pyramid with any number of sides. [2] The numbers of points in the base and in layers parallel to the base are given by polygonal numbers of the given number of sides, while the numbers of points in each triangular side is ...

  5. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure : not itself an element of a polytope, but a diagram showing how the elements meet.

  6. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices. The tetrahedron is the simplest of all the ordinary convex polyhedra .

  7. Cannonball problem - Wikipedia

    en.wikipedia.org/wiki/Cannonball_problem

    A triangular-pyramid version of the cannonball problem, which is to yield a perfect square from the N th Tetrahedral number, would have N = 48. That means that the (24 × 2 = ) 48th tetrahedral number equals to (70 2 × 2 2 = 140 2 = ) 19600. This is comparable with the 24th square pyramid having a total of 70 2 cannonballs. [5]

  8. Triangular bipyramid - Wikipedia

    en.wikipedia.org/wiki/Triangular_bipyramid

    A triangular bipyramid is a hexahedron with six triangular faces constructed by attaching two tetrahedra face-to-face. The same shape is also known as a triangular dipyramid [1] [2] or trigonal bipyramid. [3] If these tetrahedra are regular, all faces of a triangular bipyramid are equilateral.

  9. Triaugmented dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Triaugmented_dodecahedron

    In geometry, the triaugmented dodecahedron is one of the Johnson solids (J 61).It can be seen as a dodecahedron with three pentagonal pyramids (J 2) attached to nonadjacent faces.