I do not know solution using AMScd. (As far as I know, AMScd only has horizontal and vertical arrows.)
If you are familiar with xypic, you could use this syntax and include it as a picture. (You create it either locally on your computer or using some online tool, for example, the presheaf website.) It is reasonable to include somewhere (maybe as a comment in your post) the source of the diagram, too.
For example, you can get this diagram: http://presheaf.com/?d=d3j4t1z705k6j154i2k5u2v4y113a4v36 http://presheaf.com/cache/d3j4t1z705k6j154i2k5u2v4y113a4v36.png
S^{n-1} \ar[r]^{\subseteq} \ar[d]_h & D^n \ar[dd] \ar@/^/[rddd]^q & \\
S^{n-1} \ar[d] & \\
D^n \ar[r] \ar@/_/[rrd]_p & \Sigma^n(h) \ar@{-->}[rd] & \\
&& S^n
Another popular package to create commutative diagrams is tikzCD - I am pretty sure that somebody familiar with it can provide you source code to get your diagram. (And also for this package you can do it either online or locally.)
See also:
- How to draw a commutative diagram? - one of the answers mentions xypic and presheaf
- Triangle commutative diagram does not work here at MO and Is it possible to use tikzcd code in MO posts? on MathOverflow Meta
- Posts on the main site with links to presheaf
- Your professional $\LaTeX$ experiences that saves your time in typesetting - an answer with a link to online tikzcd editor