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The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron, the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid".
Each base edge and apex form a triangle, called a lateral face. A pyramid is a conic solid with a polygonal base. Many types of pyramids can be found by determining the shape of bases, either by based on a regular polygon (regular pyramids) or by cutting off the apex (truncated pyramid).
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.
Alternatively, if you expand each of five cubes by moving the faces away from the origin the right amount and rotating each of the five 72° around so they are equidistant from each other, without changing the orientation or size of the faces, and patch the pentagonal and triangular holes in the result, you get a rhombicosidodecahedron ...
The base of a pyramid can be of any polygon shape, such as triangular or quadrilateral, and its lines either filled or stepped. A pyramid has the majority of its mass closer to the ground [3] with less mass towards the pyramidion at the apex. This is due to the gradual decrease in the cross-sectional area along the vertical axis with increasing ...
The elongated triangular bipyramid is constructed from a triangular prism by attaching two tetrahedrons onto its bases, a process known as the elongation. [1] These tetrahedrons cover the triangular faces so that the resulting polyhedron has nine faces (six of them are equilateral triangles and three of them are squares), fifteen edges, and eight vertices. [2]
An elongated triangular pyramid with edge length has a height, by adding the height of a regular tetrahedron and a triangular prism: [4] (+). Its surface area can be calculated by adding the area of all eight equilateral triangles and three squares: [2] (+), and its volume can be calculated by slicing it into a regular tetrahedron and a prism, adding their volume up: [2]: ((+)).
Triangular pyramid: Y 3 (A tetrahedron is a special pyramid) T = Y 3; O = aT (ambo tetrahedron) C = jT (join tetrahedron) I = sT (snub tetrahedron) D = gT (gyro tetrahedron) Triangular antiprism: A 3 (An octahedron is a special antiprism) O = A 3; C = dA 3; Square prism: P 4 (A cube is a special prism) C = P 4; Pentagonal antiprism: A 5. I = k ...