Full Answer
How many diagonals does a dodecahedron have?
A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of twelve regular pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids. It has 12 faces, 20 vertices, 30 edges, and 160 diagonals (60 face diagonals, 100 space diagonals). Click to see full answer.
What is the difference between regular dodecahedron and pyritohedron?
In crystallography, two important dodecahedra can occur as crystal forms in some symmetry classes of the cubic crystal system that are topologically equivalent to the regular dodecahedron but less symmetrical: the pyritohedron with pyritohedral symmetry, and the tetartoid with tetrahedral symmetry :
Is a dodecahedron a convex polyhedron?
The convex regular dodecahedron is one of the five regular Platonic solids and can be represented by its Schläfli symbol {5, 3}. The dual polyhedron is the regular icosahedron {3, 5}, having five equilateral triangles around each vertex.
What is a dodecahedron made of?
In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid.
How many parallel does a trapezoid?
one pairA trapezoid has one pair of parallel sides and a parallelogram has two pairs of parallel sides.
How many parallel sides can a Pentagon have?
A pentagon has no parallel or perpendicular side. Coming to the next question, how many equal sides does a regular pentagon have? All of them. A regular pentagon has all its five slides of equal length.
How many sides does a dodecahedron have?
twelve facesShown in the above figure are the three-dimensional objects and their flattened one-, two-dimensional images. From left to right the solids are tetrahedron (four sides), cube (six sides), octahedron (eight faces), dodecahedron (twelve faces), and icosahedron (twenty faces).
What is a 12 sided 3d shape called?
In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid.
How many parallel lines does a square have?
two setsA square is a quadrilateral with 4 equal sides and 4 right angles. A shape with four sides of equal length. The shape has two sets of parallel sides and has four right angles.
How many parallel lines does a octagon have?
A regular octagon has 4 pairs of parallel sides.
What do you call a 20 sided shape?
In geometry, an icosagon or 20-gon is a twenty-sided polygon. The sum of any icosagon's interior angles is 3240 degrees.
How many faces are on a dodecahedron?
12Dodecahedron / Number of faces
How many angles does a dodecahedron have?
Table of polyhedron dihedral anglesNameSchläfli symboldihedral angle – exact in bold, else approximate (degrees)Platonic solids (regular convex)Octahedron{3,4}109.471°Dodecahedron{5,3}116.565°Icosahedron{3,5}138.190°47 more rows
What is a 12 sided prism called?
dodecagonA dodecagon is a 12-sided polygon.
What is a 1000 sided shape called?
chiliagonIn geometry, a chiliagon (/ˈkɪliəɡɒn/) or 1000-gon is a polygon with 1,000 sides. Philosophers commonly refer to chiliagons to illustrate ideas about the nature and workings of thought, meaning, and mental representation.
What is a 100 sided 3d shape called?
Zocchihedron is the label of a 100-sided die, a 3d shape. If a 3d shape with 100 faces is called hecatohedron. In case of two dimensional shapes, a shape with 100 sides is called Hectogon. The relationship between the number of faces, edges and vertices of a 3d shape is given by: F + V = E + 2.
How many faces does a dodecahedron have?
In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120.
What is the unique feature of a dodecahedron?
While the regular dodecahedron shares many features with other Platonic solids, one unique property of it is that one can start at a corner of the surface and draw an infinite number of straight lines across the figure that return to the original point without crossing over any other corner.
What is a rhombic dodecahedron?
Rhombic dodecahedron. Rhombic dodecahedron. The rhombic dodecahedron is a zonohedron with twelve rhombic faces and octahedral symmetry. It is dual to the quasiregular cuboctahedron (an Archimedean solid) and occurs in nature as a crystal form. The rhombic dodecahedron packs together to fill space.
How many faces does a tetartoid have?
A tetartoid can be created by enlarging 12 of the 24 faces of a dyakis dodecahedron . (The tetartoid shown here is based on one that is itself created by enlarging 24 of the 48 faces of the disdyakis dodecahedron .) Chiral tetartoids based on the dyakis dodecahedron in the middle. Crystal model.
How many vertices does a pyritohedron have?
Like the regular dodecahedron, it has twelve identical pentagonal faces, with three meeting in each of the 20 vertices (see figure). However, the pentagons are not constrained to be regular, and the underlying atomic arrangement has no true fivefold symmetry axis. Its 30 edges are divided into two sets – containing 24 and 6 edges of the same length. The only axes of rotational symmetry are three mutually perpendicular twofold axes and four threefold axes.
What degree of freedom does a pyritohedron have?
The pyritohedron has a geometric degree of freedom with limiting cases of a cubic convex hull at one limit of collinear edges, and a rhombic dodecahedron as the other limit as 6 edges are degenerated to length zero. The regular dodecahedron represents a special intermediate case where all edges and angles are equal.
How to divide a cube into a pyritohedron?
A cube can be divided into a pyritohedron by bisecting all the edges, and faces in alternate directions. A regular dodecahedron is an intermediate case with equal edge lengths. A rhombic dodecahedron is a degenerate case with the 6 crossedges reduced to length zero. Self-intersecting equilateral dodecahedron.
How many faces does a dodecahedron have?
A dodecahedron is a polyhedron with 12 faces. In the figure below are 2 different types of dodecahedrons. The prefix "dodeca" means twelve. Because of their complex nature, a dodecahedron is a shape that is not commonly seen in everyday life.
How to find the surface area of a dodecahedron?
Surface area of a regular dodecahedron. We can find the area of one of the faces and multiply it by twelve to find the total surface area of a regular dodecahedron. A regular pentagon with side length, e (also the length of the edges of a regular dodecahedron), has an area, A, of.