Simple multiple-sided solids {polyhedron, solid}| have genus zero.
Faces can meet at lines {edge, polyhedron}.
Plane polygons {face, polyhedron} can bound solids.
Three or more edges can meet at points {vertex, polyhedron}.
Polyhedrons {Csaszar polyhedron} can model seven-color maps of toruses, finite projective planes, and error-correcting binary codes, when used as Hadamard matrices {Room square}.
Polyhedrons {regular polyhedron} {regular solid} {Platonic solid} can have same regular polygon for all faces: four equilateral triangles {regular tetrahedron}, six squares {cube, Platonic solid}, six regular hexagons {regular hexahedron}, eight equilateral triangles {regular octahedron}, twelve regular pentagons {regular dodecahedron}, and twenty equilateral triangles {regular icosahedron}. All vertices are on circumscribed sphere. Concave regular polyhedrons are small stellated dodecahedron, great dodecahedron, or great icosahedron.
Congruent parallel faces {base, prism} and congruent parallelograms {lateral face}, joining corresponding base vertices, can make solids {prism}|. Lateral faces can be rectangles {right prism}. Prisms have adjacent lateral faces {prismatic surface}.
Polyhedrons {prismatoid} can have two faces that are parallel planes, with no vertices outside the faces. Lateral faces are triangles or quadrilaterals.
Prisms {prismoid} can have quadrilaterals for all lateral faces. Bases have same number of sides and vertices.
Prismatoids {pyramid} can have polygon bases, which contain all vertices except apex. Lateral faces are triangles. For tetrahedrons, bases are triangles. In regular pyramids, regular polygons can be bases and isosceles triangles can be lateral faces.
Polyhedrons {tetrahedron}| can have four faces.
Polyhedrons {pentahedron}| can have five faces.
Polyhedrons {diamond} can have six equal equilateral triangle faces. Diamonds are two tetrahedrons that share a face.
Polyhedrons {hexahedron} can have six faces.
Polyhedrons can have six rhombus faces {rhombohedron}|.
Polyhedrons {octahedron}| can have eight faces.
Polyhedrons {dodecahedron}| can have 12 faces.
Polyhedrons {icosahedron}| can have 20 faces.
Concave regular polyhedrons {Kepler-Poinsot concave solid} can be small stellated dodecahedron, great dodecahedron, or great icosahedron.
Concave regular polyhedrons can have 12 regular pentagons {great dodecahedron}.
Concave regular polyhedrons can have 20 equilateral triangles {great icosahedron}.
Concave regular polyhedrons can have 12 regular pentagons {small stellated dodecahedron}.
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0225