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  2. Table of polyhedron dihedral angles - Wikipedia

    en.wikipedia.org/wiki/Table_of_polyhedron...

    The dihedral angles for the edge-transitive polyhedra are: Picture Name Schläfli symbol Vertex/Face configuration exact dihedral angle ... Tetrahedron {3,3} (3.3.3)

  3. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    A space-filling tetrahedral disphenoid inside a cube. Two edges have dihedral angles of 90°, and four edges have dihedral angles of 60°. A disphenoid is a tetrahedron with four congruent triangles as faces; the triangles necessarily have all angles acute. The regular tetrahedron is a special case of a disphenoid.

  4. Trigonometry of a tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Trigonometry_of_a_tetrahedron

    The 6 edge lengths - associated to the six edges of the tetrahedron. The 12 face angles - there are three of them for each of the four faces of the tetrahedron. The 6 dihedral angles - associated to the six edges of the tetrahedron, since any two faces of the tetrahedron are connected by an edge.

  5. Ideal polyhedron - Wikipedia

    en.wikipedia.org/wiki/Ideal_polyhedron

    This fact can be used to calculate the dihedral angles themselves for a regular or edge-symmetric ideal polyhedron (in which all these angles are equal), by counting how many edges meet at each vertex: an ideal regular tetrahedron, cube or dodecahedron, with three edges per vertex, has dihedral angles = / = (), an ideal regular octahedron or ...

  6. Dihedral angle - Wikipedia

    en.wikipedia.org/wiki/Dihedral_angle

    A dihedral angle is the angle between two intersecting planes or half-planes. It is a plane angle formed on a third plane, perpendicular to the line of intersection between the two planes or the common edge between the two half-planes. In higher dimensions, a dihedral angle represents the angle between two hyperplanes.

  7. Solid angle - Wikipedia

    en.wikipedia.org/wiki/Solid_angle

    where ranges over all six of the dihedral angles between any two planes that contain the tetrahedral faces OAB, OAC, OBC and ABC. [5] A useful formula for calculating the solid angle of the tetrahedron at the origin O that is purely a function of the vertex angles θ a, θ b, θ c is given by L'Huilier's theorem [6] [7] as

  8. Truncated tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Truncated_tetrahedron

    Given the edge length .The surface area of a truncated tetrahedron is the sum of 4 regular hexagons and 4 equilateral triangles' area, and its volume is: [2] =, =.. The dihedral angle of a truncated tetrahedron between triangle-to-hexagon is approximately 109.47°, and that between adjacent hexagonal faces is approximately 70.53°.

  9. Rhombicosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombicosidodecahedron

    Dihedral angle: 3-4: 159°05′41″ (159.09°) 4-5: 148°16′57″ (148.28°) ... This projection is conformal, preserving angles but not areas or lengths. Straight ...