define a quasi-regular polyhedron - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Geometry : 3-D Euclidean : Creating Objects : geom3d/QuasiRegularPolyhedron

geom3d[QuasiRegularPolyhedron] - define a quasi-regular polyhedron

Calling Sequence

QuasiRegularPolyhedron(gon, sch, o, r)

cuboctahedron(gon, o, r)

icosidodecahedron(gon, o, r)

Parameters

gon

-

the name of the polyhedron to be created

sch

-

Schlafli symbol

o

-

point

r

-

positive number, an equation

Description

• 

A quasi-regular polyhedron is defined as having regular faces, while its vertex figures, though not regular, are cyclic and equiangular (that is, has alternate sides and can be inscribed in circles).

• 

There are two quasi-regular polyhedra: cuboctahedron and icosidodecahedron.

• 

In Maple, one can define a quasi-regular polyhedron by using the command QuasiRegularPolyhedron(gon, sch, o, r) where gon is the name of the polyhedron to be defined, sch the Schlafli symbol, o the center of the polyhedron.

• 

When r is a positive number, it specifies the radius of the circum-sphere. When r is an equation, the left-hand side is one of radius, side, or mid_radius, and the right-hand side specifies the radius of the circum-sphere, the side, or the mid-radius (respectively) of the quasi-regular polyhedron to be constructed.

• 

The Schlafli symbol can be one of the following:

Maple's Schlafli

Polyhedron type

[[3],[4]]

cuboctahedron

[[3],[5]]

icosidodecahedron

• 

Another way to define a quasi-regular polyhedron is to use the command PolyhedronName(gon, o, r) where PolyhedronName is either cuboctahedron or icosidodecahedron.

• 

To access the information relating to a quasi-regular polyhedron gon, use the following function calls:

center(gon)

returns the center of the circum-sphere of gon.

faces(gon)

returns the faces of gon, each face is represented

 

as a list of coordinates of its vertices.

form(gon)

returns the form of gon.

radius(gon)

returns the radius of the circum-sphere of gon.

schlafli(gon)

returns the Schlafli symbol of gon.

sides(gon)

returns the length of the edges of gon.

vertices(gon)

returns the coordinates of vertices of gon.

Examples

withgeom3d:

Define an icosidodecahedron with center (0,0,0), radius of the circum-sphere 1

icosidodecahedront,pointo,0,0,0,1

t

(1)

Access information relating to the icosidodecahedron t:

centert

o

(2)

formt

icosidodecahedron3d

(3)

radiust

1

(4)

schlaflit

3,5

(5)

sidest

255+5

(6)

Define a cuboctahedron with center (1,1,1), radius 2

QuasiRegularPolyhedroni,3,4,pointo,1,1,1,1

i

(7)

formi

cuboctahedron3d

(8)

See Also

geom3d[Archimedean], geom3d[polyhedra], geom3d[RegularPolyhedron], geom3d[stellate]


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam