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  2. Table of polyhedron dihedral angles - Wikipedia

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

    Name Schläfli symbol Vertex/Face configuration exact dihedral angle (radians) dihedral angle – exact in bold, else approximate (degrees) Platonic solids (regular convex) Tetrahedron {3,3} (3.3.3) arccos (⁠ 1 / 3 ⁠) 70.529° Hexahedron or Cube {4,3} (4.4.4) arccos (0) = ⁠ π / 2 ⁠ 90° Octahedron {3,4} (3.3.3.3) arccos (-⁠ 1 / 3 ...

  3. Dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Dodecahedron

    In geometry, a dodecahedron (from Ancient Greek δωδεκάεδρον (dōdekáedron); from δώδεκα (dṓdeka) 'twelve' and ἕδρα (hédra) 'base, seat, face') or duodecahedron [1] is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid.

  4. Regular dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Regular_dodecahedron

    A regular dodecahedron or pentagonal dodecahedron [notes 1] is a dodecahedron composed of regular pentagonal faces, three meeting at each vertex. It is an example of Platonic solids, described as cosmic stellation by Plato in his dialogues, and it was used as part of Solar System proposed by Johannes Kepler. However, the regular dodecahedron ...

  5. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    This is left blank for non-orientable polyhedra and hemipolyhedra (polyhedra with faces passing through their centers), for which the density is not well-defined. Note on Vertex figure images: The white polygon lines represent the "vertex figure" polygon. The colored faces are included on the vertex figure images help see their relations.

  6. Rhombic dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombic_dodecahedron

    The rhombic dodecahedron can be decomposed into six congruent (but non-regular) square dipyramids meeting at a single vertex in the center; these form the images of six pairs of the 24-cell's octahedral cells. The remaining 12 octahedral cells project onto the faces of the rhombic dodecahedron.

  7. Small stellated dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Small_stellated_dodecahedron

    The critical angle is atan(2) above the dodecahedron face. If we regard it as having 12 pentagrams as faces, with these pentagrams meeting at 30 edges and 12 vertices, we can compute its genus using Euler's formula V − E + F = 2 − 2 g {\displaystyle V-E+F=2-2g} and conclude that the small stellated dodecahedron has genus 4.

  8. What time is Jimmy Carter's funeral service? See full ... - AOL

    www.aol.com/news/time-jimmy-carters-funeral-see...

    After days of services honoring former President Jimmy Carter, an official state funeral is set for Thursday at the Washington National Cathedral in Washington, D.C. Carter's state funeral is set ...

  9. Rhombicosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombicosidodecahedron

    In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.

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