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Related Pages
Related Symbols
CirclePoints
SpherePoints
Related Categories
Creative Arts
Visualization & Graphics
Mandala-Like Figures from Joining Points
Example Notebook
Open in Cloud
Download Notebook
Here are 5 points arranged around a circle:
I
n
[
1
]
:
=
G
r
a
p
h
i
c
s
[
P
o
i
n
t
[
C
i
r
c
l
e
P
o
i
n
t
s
[
5
]
]
]
O
u
t
[
1
]
=
This joins the points in pairs:
I
n
[
2
]
:
=
G
r
a
p
h
i
c
s
[
L
i
n
e
[
T
u
p
l
e
s
[
C
i
r
c
l
e
P
o
i
n
t
s
[
5
]
,
2
]
]
]
O
u
t
[
2
]
=
Here's how
T
u
p
l
e
s
works, picking all possible pairs out of
{
a
,
b
,
c
}
:
I
n
[
3
]
:
=
T
u
p
l
e
s
[
{
a
,
b
,
c
}
,
2
]
O
u
t
[
3
]
=
{
{
a
,
a
}
,
{
a
,
b
}
,
{
a
,
c
}
,
{
b
,
a
}
,
{
b
,
b
}
,
{
b
,
c
}
,
{
c
,
a
}
,
{
c
,
b
}
,
{
c
,
c
}
}
Here's what it does picking from
{
a
,
b
,
c
,
d
}
:
I
n
[
4
]
:
=
T
u
p
l
e
s
[
{
a
,
b
,
c
,
d
}
,
2
]
O
u
t
[
4
]
=
{
{
a
,
a
}
,
{
a
,
b
}
,
{
a
,
c
}
,
{
a
,
d
}
,
{
b
,
a
}
,
{
b
,
b
}
,
{
b
,
c
}
,
{
b
,
d
}
,
{
c
,
a
}
,
{
c
,
b
}
,
{
c
,
c
}
,
{
c
,
d
}
,
{
d
,
a
}
,
{
d
,
b
}
,
{
d
,
c
}
,
{
d
,
d
}
}
Join all possible pairs of 4 points:
I
n
[
5
]
:
=
G
r
a
p
h
i
c
s
[
L
i
n
e
[
T
u
p
l
e
s
[
C
i
r
c
l
e
P
o
i
n
t
s
[
4
]
,
2
]
]
]
O
u
t
[
5
]
=
6 points:
I
n
[
6
]
:
=
G
r
a
p
h
i
c
s
[
L
i
n
e
[
T
u
p
l
e
s
[
C
i
r
c
l
e
P
o
i
n
t
s
[
6
]
,
2
]
]
]
O
u
t
[
6
]
=
7 points:
I
n
[
7
]
:
=
G
r
a
p
h
i
c
s
[
L
i
n
e
[
T
u
p
l
e
s
[
C
i
r
c
l
e
P
o
i
n
t
s
[
7
]
,
2
]
]
]
O
u
t
[
7
]
=
11 points:
I
n
[
8
]
:
=
G
r
a
p
h
i
c
s
[
L
i
n
e
[
T
u
p
l
e
s
[
C
i
r
c
l
e
P
o
i
n
t
s
[
1
1
]
,
2
]
]
]
O
u
t
[
8
]
=
50 points:
I
n
[
9
]
:
=
G
r
a
p
h
i
c
s
[
L
i
n
e
[
T
u
p
l
e
s
[
C
i
r
c
l
e
P
o
i
n
t
s
[
5
0
]
,
2
]
]
]
O
u
t
[
9
]
=
With an odd number of points---like 49---the center is white:
I
n
[
1
0
]
:
=
G
r
a
p
h
i
c
s
[
L
i
n
e
[
T
u
p
l
e
s
[
C
i
r
c
l
e
P
o
i
n
t
s
[
4
9
]
,
2
]
]
]
O
u
t
[
1
0
]
=
The 3D Case
(
9
)
S
p
h
e
r
e
P
o
i
n
t
s
distributes points as uniformly as possible on a sphere:
I
n
[
1
]
:
=
G
r
a
p
h
i
c
s
3
D
[
P
o
i
n
t
[
S
p
h
e
r
e
P
o
i
n
t
s
[
2
0
]
]
]
O
u
t
[
1
]
=
Join pairs of points in 3D:
I
n
[
2
]
:
=
G
r
a
p
h
i
c
s
3
D
[
L
i
n
e
[
T
u
p
l
e
s
[
S
p
h
e
r
e
P
o
i
n
t
s
[
2
0
]
,
2
]
]
]
O
u
t
[
2
]
=
The figure is an icosahedron:
Here is a list of the Platonic solids:
Here are pictures of them:
There are other polyhedra that aren't Platonic:
This joins pairs of 25 points in 3D:
The corresponding result for 20 points:
See Also
RandomMandala
Related Symbols
CirclePoints
SpherePoints
Publisher Information
Contributed by:
Stephen Wolfram
