Snub disphenoid

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. )

External links

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


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • Disphenoid — The tetragonal and digonal disphenoids can be positioned inside a cuboid bisecting two opposite faces. All four faces are isosceles triangles. Both have four equal edges going around the sides. The digonal has two sets of isosceles triangle faces …   Wikipedia

  • Snub polyhedron — A snub polyhedron is a polyhedron obtained by adding extra triangles around each vertex. Chiral snub polyhedra do not have reflection symmetry and hence have two enantiomorphous forms which are reflections of each other. Their symmetry groups are …   Wikipedia

  • Johnson solid — The elongated square gyrobicupola (J37), a Johnson solid …   Wikipedia

  • Polyèdre adouci — En géométrie, un polyèdre adouci est un polyèdre obtenu en écartant les faces d un polyèdre et en comblant les trous par des triangles équilatéraux. Souvent, cela consiste à remplacer chaque sommet du polyèdre par un triangle équilatéral et… …   Wikipédia en Français

  • List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

  • Deltahedron — This is a truncated tetrahedron with hexagons subdivided into triangles. This figure is not a deltahedron since coplanar faces are not allowed within the definition. A deltahedron (plural deltahedra) is a polyhedron whose faces are all… …   Wikipedia

  • Coordination geometry — The term coordination geometry is used in a number of related fields of chemistry and solid state chemistry/physics. Contents 1 Molecules 2 Inorganic coordination complexes 3 Crystallography usage 4 …   Wikipedia

  • Octahedron — For the album by The Mars Volta, see Octahedron (album). Regular Octahedron (Click here for rotating model) Type Platonic solid Elements F = 8, E = 12 V = 6 (χ = 2) Faces by sides …   Wikipedia

  • Dodecahedron — Regular Dodecahedron (Click here for rotating model) Type Platonic solid Elements F = 12, E = 30 V = 20 (χ = 2) Faces by sides 12{5} …   Wikipedia

  • Polyhedron — Polyhedra redirects here. For the relational database system, see Polyhedra DBMS. For the game magazine, see Polyhedron (magazine). For the scientific journal, see Polyhedron (journal). Some Polyhedra Dodecahedron (Regular polyhedron) …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”