# Snub disphenoid

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Snub disphenoid

Infobox Polyhedron with net

Polyhedron_Type=Johnson
J83 - J84 - J85
Face_List=4+8 triangles
Edge_Count=18
Vertex_Count=8
Symmetry_Group="D2d"| Vertex_List=4(34)
4(35)
Dual=-
Property_List=convex, deltahedron
Net_

In geometry, the snub disphenoid is one of the Johnson solids ("J"84). It is a three-dimensional solid that has only equilateral triangles as faces, and is therefore a deltahedron. It is not a regular polyhedron because some vertices have four faces and others have five. It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids.

The 92 Johnson solids were named and described by Norman Johnson in 1966.

It was called a Siamese dodecahedron in the paper by Freudenthal and Waerden which first described it in 1947 in the set of convex deltahedra.

References

* * Freudenthal, H. and van der Waerden, B. L. "Over een bewering van Euclides". ("On an Assertion of Euclid") Simon Stevin 25, 115—128, 1947. (They showed that there are just 8 convex deltahedra. )

*
** MathWorld | urlname=SnubDisphenoid | title=Snub disphenoid

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