Deltoidal icositetrahedron

A deltoidal icositetrahedron is a Catalan solid Catalan solid

In mathematics [i], a Catalan solid, or Archimedean dual, is a dual polyhedron [i] to an Archimedean solid [i] ...

which looks a bit like an overinflated cube Cube

A cube is a three-dimensional [i] Platonic solid [i] composed of six square [i] ...

. Its dual polyhedron Dual polyhedron

In geometry [i], polyhedra [i] are associated into pairs called duals, where the vertices [i] ...

is the rhombicuboctahedron Rhombicuboctahedron

The rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid [i] with eight triangular [i] ...

. The 24 faces are deltoids or kites Kite

A kite is a flying tethered man-made object....

, not trapezoid Trapezoid

A trapezoid or trapezium is a quadrilateral [i] two of whose sides are parallel [i] to ea ...

s; the trapezohedron Trapezohedron

The n-gonal trapezohedron or deltohedron is the dual polyhedron [i] of a regular n-gonal antiprism [i] ...

is similarly misnamed. The trapezoidal icositetrahedron is a crystal habit Crystal habit

In mineralogy [i], shape and size give rise to descriptive terms applied to the typical appearance, or habi ...

often formed by the mineral analcime Analcite

Analcite or analcime is a white, grey, or colourless tectosilicate [i] mineral [i] ...

and occasionally garnet Garnet

The garnet group of mineral [i]s show crystal [i]s with a habit of rhombic dodecahedron [i]s and trapezohedron [i] ...

. The shape is often called a trapezohedron Trapezohedron

The n-gonal trapezohedron or deltohedron is the dual polyhedron [i] of a regular n-gonal antiprism [i] ...

in mineral contexts, although in solid geometry that name refers to a particular class of polyhedron Polyhedron

A polyhedron is a geometric shape which in mathematics [i] is defined by three related meanings. ...

. The Shining Trapezohedron of the fictional Lovecraft Mythos was probably intended to refer to a crystal Crystal

In chemistry [i] and mineralogy [i], a crystal is a solid [i] in which the constituent atom [i]s, molecule [i] ...

of this shape.

Discussions

Discussion Features

Ask a question about 'Deltoidal icositetrahedron'

Start a new discussion about 'Deltoidal icositetrahedron'

Answer questions about 'Deltoidal icositetrahedron'

'Deltoidal icositetrahedron' discussion forum

Encyclopedia

Deltoidal icositetrahedron
Click on picture for large version. Click for spinning version.
Type	Catalan Catalan solid In mathematics [i], a Catalan solid, or Archimedean dual, is a dual polyhedron [i] to an Archimedean solid [i] ...
Face polygon	kite Kite A kite is a flying tethered man-made object....
Faces	24
Edges	48
Vertices	26 = 6 + 8 + 12
Face configuration Face configuration In geometry, a face configuration is notational description of a face-uniform [i] polyhedron [i]. ...	V3.4.4.4
Symmetry group Symmetry group The symmetry [i] group of an object is the group [i] of all isometries [i] under which it is invariant [i] ...	octahedral
Dual polyhedron Dual polyhedron In geometry [i], polyhedra [i] are associated into pairs called *duals*, where the vertices [i] ...	rhombicuboctahedron Rhombicuboctahedron The rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid [i] with eight triangular [i] ...
Properties	convex, face-uniform

A deltoidal icositetrahedron is a Catalan solid Catalan solid

In mathematics [i], a Catalan solid, or Archimedean dual, is a dual polyhedron [i] to an Archimedean solid [i] ...

which looks a bit like an overinflated cube Cube

A cube is a three-dimensional [i] Platonic solid [i] composed of six square [i] ...

. Its dual polyhedron Dual polyhedron

In geometry [i], polyhedra [i] are associated into pairs called duals, where the vertices [i] ...

is the rhombicuboctahedron Rhombicuboctahedron

The rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid [i] with eight triangular [i] ...

.

The 24 faces are deltoids or kites Kite

A kite is a flying tethered man-made object....

, not trapezoid Trapezoid

A trapezoid or trapezium is a quadrilateral [i] two of whose sides are parallel [i] to ea ...

s; the trapezohedron Trapezohedron

The n-gonal trapezohedron or deltohedron is the dual polyhedron [i] of a regular n-gonal antiprism [i] ...

is similarly misnamed.

The trapezoidal icositetrahedron is a crystal habit Crystal habit

In mineralogy [i], shape and size give rise to descriptive terms applied to the typical appearance, or habi...

often formed by the mineral analcime Analcite

Analcite or analcime is a white, grey, or colourless tectosilicate [i] mineral [i] ...

and occasionally garnet Garnet

The garnet group of mineral [i]s show crystal [i]s with a habit of rhombic dodecahedron [i]s and trapezohedron [i] ...

. The shape is often called a trapezohedron Trapezohedron

In chemistry [i] and mineralogy [i], a crystal is a solid [i] in which the constituent atom [i]s, molecule [i] ...

of this shape.

Deltoidal icositetrahedron

Discussions

Encyclopedia

See also