A Platonic Solid is a 3D shape where:

• each face is the same regular polygon
• the same number of polygons meet at each vertex (corner)

Number of faces around a vertex. Let’s make a table enumerating how many faces, edges, and vertices are in each of the five Platonic Solids. Platonic Solid Faces Edges Vertices Tetrahedron 4 Cube 6 Octahedron 8 Dodecahedron 12 Icosahedron 20 Table 1: Platonic Solids: number of faces, edges, and vertices. Fill in the rest of the. Vertices, Edges and Faces. A vertex is a corner. An edge is a line segment between faces. A face is a single flat surface. Let us look more closely at each of those: Vertices. A vertex (plural: vertices) is a point where two or more line segments meet. It is a Corner. This tetrahedron has 4 vertices.

Example: the Cube is a Platonic Solid

There are only five platonic solids.

The Platonic Solids

For each solid we have two printable nets (with and without tabs). You can make models with them!
Print them on a piece of card, cut them out, tape the edges, and you will have your own platonic solids.

The following polyhedra are combinatorially equivalent to the regular polyhedron. They all have six vertices, eight triangular faces, and twelve edges that correspond one-for-one with the features of a regular octahedron. Triangular: Two faces are equilateral, lie on parallel planes, and have a common axis of symmetry.

The other six triangles are isosceles. Tetragonal, in which at least one of the equatorial quadrilaterals lies on a plane. The regular octahedron is a special case in which all three quadrilaterals are planar squares., a non-convex polyhedron that cannot be partitioned into tetrahedra without introducing new vertices., a non-convex self-crossingOther convex octahedraMore generally, an octahedron can be any polyhedron with eight faces. The regular octahedron has 6 vertices and 12 edges, the minimum for an octahedron; irregular octahedra may have as many as 12 vertices and 18 edges.There are 257 topologically distinct convex octahedra, excluding mirror images. More specifically there are 2, 11, 42, 74, 76, 38, 14 for octahedra with 6 to 12 vertices respectively. (Two polyhedra are 'topologically distinct' if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.)Some better known irregular octahedra include the following:.: Two faces are parallel regular hexagons; six squares link corresponding pairs of hexagon edges.

Heptagonal: One face is a heptagon (usually regular), and the remaining seven faces are triangles (usually isosceles). It is not possible for all triangular faces to be equilateral.: The four faces from the tetrahedron are truncated to become regular hexagons, and there are four more equilateral triangle faces where each tetrahedron vertex was truncated.: The eight faces are congruent.Octahedra in the physical world. t.SphericalEuclid.Compact hyper.Paraco.Noncompact hyperbolic3 12i3 9i3 6i3 3iTetratetrahedronThe regular octahedron can also be considered a tetrahedron – and can be called a tetratetrahedron. This can be shown by a 2-color face model. With this coloring, the octahedron has.Compare this truncation sequence between a tetrahedron and its dual::, (.332)3,3 +, (332)Duals to uniform polyhedraThe above shapes may also be realized as slices orthogonal to the long diagonal of a. If this diagonal is oriented vertically with a height of 1, then the first five slices above occur at heights r, 3 / 8, 1 / 2, 5 / 8, and s, where r is any number in the range 0. Finbow, Arthur S.; Hartnell, Bert L.; Nowakowski, Richard J.; (2010).

'On well-covered triangulations. Discrete Applied Mathematics. 158 (8): 894–912. Archived from on 17 November 2014. Retrieved 14 August 2016. CS1 maint: archived copy as title.

Killing floor 2 release date. Klein, Douglas J. Croatica Chemica Acta. 75 (2): 633–649. Retrieved 30 September 2006., Third edition, (1973), Dover edition, (Chapter V: The Kaleidoscope, Section: 5.7 Wythoff's construction).External links.