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  2. Dihedral angle - Wikipedia

    en.wikipedia.org/wiki/Dihedral_angle

    Free energy diagram of n-butane as a function of dihedral angle. In stereochemistry , a torsion angle is defined as a particular example of a dihedral angle, describing the geometric relation of two parts of a molecule joined by a chemical bond .

  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 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. The 4 solid angles - associated to each point of the tetrahedron.

  5. Lists of uniform tilings on the sphere, plane, and hyperbolic ...

    en.wikipedia.org/wiki/Lists_of_uniform_tilings...

    In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r. Special cases are right triangles (p q 2).

  6. 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°.

  7. Table of polyhedron dihedral angles - Wikipedia

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

    exact dihedral angle (radians) dihedral angle – exact in bold, else approximate (degrees) Platonic solids (regular convex) Tetrahedron {3,3} (3.3.3)

  8. Simplex - Wikipedia

    en.wikipedia.org/wiki/Simplex

    The triangle is the 2-simplex, a simple shape that requires two dimensions. ... from which the dihedral angles are calculated. ... The Hasse diagram of the face ...

  9. Disdyakis triacontahedron - Wikipedia

    en.wikipedia.org/wiki/Disdyakis_triacontahedron

    Coxeter diagram: Face polygon: scalene triangle: Faces: 120 ... and common dihedral angle ... Each triangle can be mapped to another triangle of the same color by ...