Set of n-gonal truncated trapezohedra | |
---|---|
![]() Example: pentagonal truncated trapezohedron (regular dodecahedron) | |
Faces | 2 n-sided polygons, 2n pentagons |
Edges | 6n |
Vertices | 4n |
Conway notation | t4dA4 t5dA5 t6dA6 |
Symmetry group | Dnd, [2+,2n], (2*n), order 4n |
Rotation group | Dn, [2,n]+, (22n), order 2n |
Dual polyhedron | gyroelongated bipyramids |
Properties | convex |
In geometry, an n-gonal truncated trapezohedron is a polyhedron formed by a n-gonal trapezohedron with n-gonal pyramids truncated from its two polar axis vertices.
The vertices exist as 4 n-gons in four parallel planes, with alternating orientation in the middle creating the pentagons.
The regular dodecahedron is the most common polyhedron in this class, being a Platonic solid, with 12 congruent pentagonal faces.
A truncated trapezohedron has all vertices with 3 faces. This means that the dual polyhedra, the set of gyroelongated dipyramids, have all triangular faces. For example, the icosahedron is the dual of the dodecahedron.
Forms[edit]
- Triangular truncated trapezohedron (Dürer's solid) – 6 pentagons, 2 triangles, dual gyroelongated triangular dipyramid
- Truncated square trapezohedron – 8 pentagons, 2 squares, dual gyroelongated square dipyramid
- Truncated pentagonal trapezohedron or regular dodecahedron – 12 pentagonal faces, dual icosahedron
- Truncated hexagonal trapezohedron – 12 pentagons, 2 hexagons, dual gyroelongated hexagonal dipyramid
- ...
- Truncated n-gonal trapezohedron – 2n pentagons, 2 n-gons, dual gyroelongated dipyramids
See also[edit]
External links[edit]
- Conway Notation for Polyhedra Try: "tndAn", where n=4,5,6... example "t5dA5" is a dodecahedron.
Well, that’s interesting to know that Psilotum nudum are known as whisk ferns. Psilotum nudum is the commoner species of the two. While the P. flaccidum is a rare species and is found in the tropical islands. Both the species are usually epiphytic in habit and grow upon tree ferns. These species may also be terrestrial and grow in humus or in the crevices of the rocks.
View the detailed Guide of Psilotum nudum: Detailed Study Of Psilotum Nudum (Whisk Fern), Classification, Anatomy, Reproduction