The dihedral angles for the edge-transitive polyhedra are: Coxeter, Regular Polytopes (1963), Macmillan Company Regular Polytopes, (3rd edition, 1973)...

number of angles associated with each Platonic solid. The dihedral angle is the interior angle between any two face planes. The dihedral angle, θ, of the...

infinite-dimensional vector space, determined from the lengths and dihedral angles of a polyhedron's edges. Another of Hilbert's problems, Hilbert's eighteenth problem...

hyperbolic tilings {p,q}, and non-right (p q r) groups. Table of polyhedron dihedral angles Vertex-transitive Face-transitive Cell-transitive Tilings...

usage. The angle between two planes (such as two adjacent faces of a polyhedron) is called a dihedral angle. It may be defined as the acute angle between...

vertices of a convex regular polyhedron all lie on a sphere. All the dihedral angles of the polyhedron are equal All the vertex figures of the polyhedron are...

\end{aligned}}} The dihedral angle of a triangular bipyramid can be obtained by adding the dihedral angle of two regular tetrahedra. The dihedral angle of a triangular...

dihedral angle of a rhombicuboctahedron can be determined by adding the dihedral angle of a square cupola and an octagonal prism: the dihedral angle of...

A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting...

almost all of the uniform polyhedra from the acute and obtuse Schwarz triangles. The numbers that can be used for the sides of a non-dihedral acute or obtuse...

sense: the exact angles and edge lengths may differ. Hart introduced the reflection operator r, that gives the mirror image of the polyhedron. This is not...

Coxeter-Dynkin diagram of the generated polyhedron contains three nodes representing the three mirrors. The dihedral angle between each pair of mirrors is encoded...

each of its vertices in the same or reverse order, all two adjacent faces have the same dihedral angle. Therefore, the cube is regular polyhedron because...

prism, the dihedral group D 3 h {\displaystyle D_{3\mathrm {h} }} of order twelve. Its dihedral angles can be calculated by adding the angles of the component...

a polyhedron, represent its dihedral angle as a rational combination of angles from the basis. Discard the coefficient for the rational multiple of π...

is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two pentagonal pyramids with regular faces to each of its pentagonal...

Regular polytope Regular polyhedron List of uniform tilings Uniform tilings in hyperbolic plane List of uniform polyhedra List of uniform polyhedra by Schwarz...

eight-sided polyhedron; many types of irregular octahedra also exist. A regular octahedron is the three-dimensional case of the more general concept of a cross-polytope...

tilings, and in polyhedrons such as the deltahedron and antiprism. It appears in real life in popular culture, architecture, and the study of stereochemistry...

are all regular polygons, it is an equilateral square pyramid. The dihedral angles between adjacent triangular faces are arccos ⁡ ( − 1 / 3 ) ≈ 109.47...

the result of truncating axial vertices of a pentagonal trapezohedron. It is also a Goldberg polyhedron because it is the initial polyhedron to construct...

gyroelongated pentagonal pyramid is a polyhedron constructed by attaching a pentagonal antiprism to the base of a pentagonal pyramid. An alternative name...

In geometry, an octagon (from Ancient Greek ὀκτάγωνον (oktágōnon) 'eight angles') is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol...

geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length)....

q , r } {\displaystyle \{p,q\},\{q,r\}} which form its cells and a dihedral angle constraint sin ⁡ π p sin ⁡ π r > cos ⁡ π q {\displaystyle \sin {\frac...

Hyperboloid Napkin ring problem Pappus's centroid theorem Paraboloid Polyhedron Defect Dihedral angle Prism Prismatoid Honeycomb Pyramid Parallelepiped Tetrahedron...

rectangles, a square's angles are right angles (90 degrees, or π/2 radians), making adjacent sides perpendicular. The area of a square is the side length...

convex and all of its faces are regular polygons, it is classified as the second Johnson solid J 2 {\displaystyle J_{2}} . The dihedral angle between two...

polyhedron with a similar name, the nonconvex great rhombicosidodecahedron. The surface area A and the volume V of the truncated icosidodecahedron of...

hexagons surround each of its vertex, denoting its vertex figure as 4 ⋅ 6 2 {\displaystyle 4\cdot 6^{2}} . The dihedral angle of a truncated octahedron...