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Learn More about
Wolfram Language
SimplicialHomology
Guides
SimplicialHomology
Symbols
BettiNumber
HomologyGroup
SimplicialAutomorphismGroup
SimplicialComplex
SimplicialCone
SimplicialIsomorphicQ
SimplicialJoin
SimplicialSuspension
SubComplexQ
Taggar`SimplicialHomology`
S
i
m
p
l
i
c
i
a
l
S
u
s
p
e
n
s
i
o
n
S
i
m
p
l
i
c
i
a
l
S
u
s
p
e
n
s
i
o
n
[
s
c
]
r
e
t
u
r
n
s
t
h
e
s
u
s
p
e
n
s
i
o
n
o
f
t
h
e
s
i
m
p
l
i
c
i
a
l
c
o
m
p
l
e
x
s
c
.
D
e
t
a
i
l
s
a
n
d
O
p
t
i
o
n
s
▪
Suspension of a simplicial complex
s
c
, denoted
S
(
s
c
)
is the join of
s
c
with a point.
▪
s
c
must be a
S
i
m
p
l
i
c
i
a
l
C
o
m
p
l
e
x
object.
▪
S
i
m
p
l
i
c
i
a
l
S
u
s
p
e
n
s
i
o
n
returns a
S
i
m
p
l
i
c
i
a
l
C
o
m
p
l
e
x
object.
Examples
(
7
)
Basic Examples
(
3
)
Find the suspension of a simplicial complex:
I
n
[
1
]
:
=
S
i
m
p
l
i
c
i
a
l
S
u
s
p
e
n
s
i
o
n
S
i
m
p
l
i
c
i
a
l
C
o
m
p
l
e
x
[
"
T
o
r
u
s
"
]
O
u
t
[
1
]
=
S
i
m
p
l
i
c
i
a
l
C
o
m
p
l
e
x
D
i
m
e
n
s
i
o
n
:
3
V
e
r
t
i
c
e
s
:
9
Cone of the 2-simplex is two tetrahedra glued along the common face:
I
n
[
1
]
:
=
S
i
m
p
l
i
c
i
a
l
S
u
s
p
e
n
s
i
o
n
S
i
m
p
l
i
c
i
a
l
C
o
m
p
l
e
x
[
"
T
r
i
a
n
g
l
e
"
]
O
u
t
[
1
]
=
S
i
m
p
l
i
c
i
a
l
C
o
m
p
l
e
x
D
i
m
e
n
s
i
o
n
:
3
V
e
r
t
i
c
e
s
:
5
I
n
[
2
]
:
=
%
[
"
1
S
k
e
l
e
t
o
n
"
]
O
u
t
[
2
]
=
Suspension of
S
i
m
p
l
i
c
i
a
l
C
o
m
p
l
e
x
[
{
"
C
i
r
c
l
e
"
,
n
}
]
is
S
i
m
p
l
i
c
i
a
l
C
o
m
p
l
e
x
[
{
"
C
i
r
c
l
e
"
,
n
+
1
}
]
:
I
n
[
1
]
:
=
H
o
m
o
l
o
g
y
G
r
o
u
p
s
n
=
S
i
m
p
l
i
c
i
a
l
C
o
m
p
l
e
x
[
{
"
C
i
r
c
l
e
"
,
2
}
]
O
u
t
[
1
]
=
0
,
1
0
,
2
I
n
[
2
]
:
=
H
o
m
o
l
o
g
y
G
r
o
u
p
S
i
m
p
l
i
c
i
a
l
S
u
s
p
e
n
s
i
o
n
[
s
n
]
O
u
t
[
2
]
=
0
,
1
0
,
2
0
,
3
P
r
o
p
e
r
t
i
e
s
&
R
e
l
a
t
i
o
n
s
(
4
)
S
e
e
A
l
s
o
S
i
m
p
l
i
c
i
a
l
C
o
m
p
l
e
x
▪
S
i
m
p
l
i
c
i
a
l
J
o
i
n
R
e
l
a
t
e
d
G
u
i
d
e
s
▪
S
i
m
p
l
i
c
i
a
l
H
o
m
o
l
o
g
y
"
"