Casting base class to templated derived class

Question

I am trying to create a map where types can be accessed based on their type. I am having issues getting the code to compile.

#include <iostream>
#include <typeindex>
#include <map>

struct ITest {
};

template <class T>
struct Test : public ITest {
};

struct Vertex {
    int x;
    int y;
    int z;
};

std::map<std::type_index, ITest> m;

template <typename T>
void add() {
    m[typeid(T)] = Test<T>();
}

template <typename T>
Test<T> get() {
    // The compiler doesn't like this line. All I'm trying to do is get the base         
    // class via the type id, then cast it to the templated derived class
    return static_cast<Test<T>>(m[typeid(T)]);
}

int main() {
    add<Vertex>();
    Test<Vertex> v = get<Vertex>();

    return 0;
}

The following is the error being generated using GCC 9.4.0 and compiling for C++17.

error: no matching function for call to ‘Test<Vertex>::Test(std::map<std::type_index, ITest>::mapped_type&)’

return static_cast<Test<T>>(m[std::type_index(typeid(T))]);

I'm not really sure what the issue with this line is. I'm indexing via the id of the type and casting the ITest to a templated Test. This question is pretty straightforward. If you can help me getting this to compile that would be great. Thanks