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Equilateral triangles, squares, regular pentagons.
It's a polyhedron. A polyhedron (plural: polyhedra) is a three - dimensional figure made up of sides called faces, each face being a polygon.
If the question is meant to ask why you cannot make a six sided Platonic solid, the answer is you can - a cube,. If the question is meant to ask why you cannot make a Platonic solid with regular hexagons, the answer is that their interior angles are all 120 degrees. A dihedral angle needs three (or more) faces to meet at a point but three hexagons add up to 360 degrees, which forms a plane - not an angle.
Any convex three dimensional figure with straight edges (or plain faces) will have polygons for bases so there is an infinity of such shapes.
Polyhedra (plural; singular = polyhedron)
triangles, squares and pentagons.
The polygons are the equilateral triangle, the square, and the regular pentagon. The faces of these platonic solids are made from the following polygons: tetrahedron - 4 triangles cube - 6 squares octahedron - 8 triangles dodecahedron - 12 pentagons icosahedron - 20 triangles
Equilateral triangles, squares, regular pentagons.
The three-dimensional platonic solid with eight faces is an octahedron.
Answering your questions one at a time.1 - What is a platonic solid?A platonic solid is one with all faces congruent polygons, meaning that they all have the same number of sides, vertices and angle size.2 - How many are there?There are only and exactly five.3 - What are their names?TetrahedronCube (but when talking about Platonic solids, it is commonly referred to as a "hexahedron").OctahedronDodecahedronIcosahedronNote: These individual platonic solids can be identified by their unique Schlafli Symbol. This is demonstrated through the following:{p,q}p = Number of vertices at each faceq = Number of faces at each vertexSo for a dodecahedron, the Shlafli Symbol would be {5,3}, because a pentagon has five {5, or p} vertices, and at any individual vertex three {3, or q} faces meet.Understand? Great!
They are prisms. The bases may be any polygons with three or more sides.
A dodecahedron. A dodecahedron is any polyhedron with twelve faces, but usually a regular dodecahedron is meant. It is a Platonic solid composed of twelve regular pentagonal faces, with three meeting at each vertex. It has twenty (20) vertexes and thirty (30) edges. The dodecahedron would be the Platonic solid with the largest volume if all were made with edges of the same length.
A three dimensional figure with polygonal faces is called a polyhedron. Specific names draw from the Latin prefixes. For example a four sided figure is a tetrahedron.
It's a polyhedron. A polyhedron (plural: polyhedra) is a three - dimensional figure made up of sides called faces, each face being a polygon.
Cone
If the question is meant to ask why you cannot make a six sided Platonic solid, the answer is you can - a cube,. If the question is meant to ask why you cannot make a Platonic solid with regular hexagons, the answer is that their interior angles are all 120 degrees. A dihedral angle needs three (or more) faces to meet at a point but three hexagons add up to 360 degrees, which forms a plane - not an angle.
Any convex three dimensional figure with straight edges (or plain faces) will have polygons for bases so there is an infinity of such shapes.