Triangular cupola
Encyclopedia
In geometry
, the triangular cupola
is one of the Johnson solid
s (J3). It can be seen as half a cuboctahedron
.
The 92 Johnson solids were named and described by Norman Johnson in 1966.
e for the volume
and surface area
can be used if all face
s are regular
, with edge length a:
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the triangular cupola
Cupola (geometry)
In geometry, a cupola is a solid formed by joining two polygons, one with twice as many edges as the other, by an alternating band of triangles and rectangles...
is one of the Johnson solid
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...
s (J3). It can be seen as half a cuboctahedron
Cuboctahedron
In geometry, a cuboctahedron is a polyhedron with eight triangular faces and six square faces. A cuboctahedron has 12 identical vertices, with two triangles and two squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such it is a quasiregular polyhedron,...
.
The 92 Johnson solids were named and described by Norman Johnson in 1966.
Formulae
The following formulaFormula
In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language....
e for the volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
and surface area
Surface area
Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve. For polyhedra the surface area is the sum of the areas of its faces...
can be used if all face
Face (geometry)
In geometry, a face of a polyhedron is any of the polygons that make up its boundaries. For example, any of the squares that bound a cube is a face of the cube...
s are regular
Regular polygon
A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...
, with edge length a:
Dual polyhedron
The dual of the triangular cupola has 12 triangular faces:| Dual triangular cupola | Net of dual |
|---|---|