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Regular polyhedron

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A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that the faces are congruent regular polygons which are assembled in the same way around each vertex.

The coccolithophore Braarudosphaera bigelowii has a regular dodecahedral structure

The radiolarian Circogonia icosahedra has a regular icosahedral structure

A myovirus typically has a regular icosahedral capsid (head) about 100 nanometers across.

Image: Tetrahedron

Polyhedron

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In geometry, a polyhedron is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.

Convex polyhedron blocks on display at the Universum museum in Mexico City

Problem 14 of the Moscow Mathematical Papyrus, on calculating the volume of a frustum

14-sided die from the Warring States period

Doppio ritratto, attributed to Jacopo de' Barbari, depicting Luca Pacioli and a student studying a glass rhombicuboctahedron half-filled with water.