English

A snub disphenoid

Noun

snub disphenoid ‎(plural snub disphenoids)

1. A non-regular convex polyhedron that has 12 equilateral triangles as faces and 18 edges and is a Johnson solid.
   • 2005, Robin Hartshorne, Geometry: Euclid and Beyond, page 457,

     For the snub disphenoid, our existence proof used the intermediate value theorem in the real numbers to argue that as AB decreases and CD increases there is a point where they become equal.

   • 2006, Andrew J. Locock, Chapter 6: Crystal chemistry of actinide phosphates and arsenates, Sergey Krivovichev, Peter Burns, Ivan Tananaev (editors), Structural Chemistry of Inorganic Actinide Compounds, page 225,

     In this structure-type, the eight-coordinate polyhedra (snub disphenoids) share edges to form a framework composed of cross-linked chains that extend along the [100] and [010] directions.

   • 2013, Thomas Hull, Project Origami: Activities for Exploring Mathematics, 2nd Edition, page 153,

     Thus, at a basic level this activity is about exploring such polyhedra, starting with the regular cases of the tetrahedron, octahedron, and icosahedron and moving into other solids like the triangular dipyramid and snub disphenoid.

Synonyms

• (polyhedron with 12 equilaterally triangular faces): Siamese dodecahedron, dodecadeltahedron

Hypernyms

• deltahedron (polyhedron with faces that are all equilateral triangles)
• dodecahedron (polyhedron with twelve faces)