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geom3d[Archimedean] - define an Archimedean solid

Calling Sequence

Archimedean(gon, sch, o, r)

TruncatedTetrahedron(gon, o, r)

TruncatedOctahedron(gon, o, r)

TruncatedHexahedron(gon, o, r)

TruncatedIcosahedron(gon, o, r)

TruncatedDodecahedron(gon, o, r)

SmallRhombicuboctahedron(gon, o, r)

SmallRhombiicosidodecahedron(gon, o, r)

GreatRhombicuboctahedron(gon, o, r)

TruncatedCuboctahedron(gon, o, r)

GreatRhombiicosidodecahedron(gon, o, r)

TruncatedIcosidodecahedron(gon, o, r)

SnubCube(gon, o, r)

SnubDodecahedron(gon, o, r)

cuboctahedron(gon, o, r)

icosidodecahedron(gon, o, r)

Parameters

gon

-

the name of the polyhedron to be created

sch

-

Schlafli symbol

o

-

a point

r

-

a positive number, an equation

Description

• 

A polyhedron is said to be uniform if its faces are regular while its vertices are all alike, i.e., every vertex can be transformed into any other by a symmetry operation.

• 

Archimedean solids are uniform polyhedra with faces of at least two kinds. Besides the infinite families of prisms and antiprisms, there are thirteen Archimedean solids.

• 

In Maple, one can define an Archimedean solid by using the command Archimedean(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 Archimedean solid to be constructed.

• 

The Schlafli symbol can be one of the following:

Maple's Schlafli

Polyhedron type

_t([3,3])

truncated tetrahedron

_t([3,4])

truncated octahedron

_t([4,3])

truncated cube

_t([3,5])

truncated icosahedron

_t([5,3])

truncated dodecahedron

[[3],[4]]

cuboctahedron

[[3],[5]]

icosidodecahedron

_r([[3],[4]])

small rhombicuboctahedron

_r([[3],[5]])

small rhombiicosidodecahedron

_t([[3],[4]])

great rhombicuboctahedron

_t([[3],[5]])

great rhombiicosidodecahedron

_s([[3],[4]])

snub cube

_s([[3],[5]])

snub dodecahedron

• 

Another way to define an Archimedean solid is to use the command PolyhedronName(gon,o,r) where PolyhedronName is one of TruncatedTetrahedron, TruncatedOctahedron, TruncatedHexahedron, TruncatedIcosahedron, TruncatedDodecahedron, SmallRhombicuboctahedron, SmallRhombiicosidodecahedron, GreatRhombicuboctahedron, TruncatedCuboctahedron, GreatRhombiicosidodecahedron, TruncatedIcosidodecahedron, SnubCube, cuboctahedron, or icosidodecahedron.

• 

To access the information relating to an Archimedean solid 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.

MidRadius(gon);

returns the mid-radius of gon, i.e., the radius

 

of the mid-sphere (the one which touches all the edges).

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 a truncated tetrahedron with center (0,0,0), radius of the circum-sphere 1

TruncatedTetrahedront,pointo,0,0,0,1

t

(1)

Access information relating to the truncated tetrahedron t:

centert

o

(2)

facest

111333,133333,133333,133333,111333,133333,133333,133333,111333,133333,133333,111333,111333,133333,133333,133333,111333,133333,133333,111333,133333,133333,133333,111333,111333,133333,133333,111333,133333,133333,133333,111333,133333,133333,133333,111333,133333,133333,111333,133333,111333,133333,133333,111333,133333,111333,133333,133333,111333,133333,133333,133333,133333,111333,133333,111333,133333,133333,111333,133333,111333,133333,133333,111333,133333,133333,133333,133333,111333,133333,133333,111333,111333,133333,133333,133333,133333,111333,133333,133333,111333,133333,111333,133333,133333,111333,133333,111333,133333,133333,111333,133333,133333,111333,133333,133333,133333,133333,111333,133333,133333,111333,133333,111333,133333,133333,111333,133333

(3)

formt

TruncatedTetrahedron3d

(4)

MidRadiust

1226332

(5)

radiust

1

(6)

schlaflit

_t3,3

(7)

sidest

233633

(8)

Define a small rhombicuboctahedron with center (1,1,1), radius sqrt(2)

Archimedeani,_r3,4,pointo,1,1,1,1

i

(9)

formi

SmallRhombicuboctahedron3d

(10)

See Also

geom3d[polyhedra], geom3d[QuasiRegularPolyhedron], geom3d[RegularPolyhedron], geom3d[stellate]


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