I believe your question asks about isotopy:

Isotopy property: A combinatorial structure (such as a combinatorial type of polytope) has the isotopy property if any two realizations with the same orientation can be deformed into each other by a continuous deformation that maintains the combinatorial type. Equivalently, the isotopy property holds for a combinatorial structure if and only if its realization space is connected.

This definition is quoted from "Basic Properties of Convex Polytopes" by Martin Henk, Jürgen Richter-Gebert, and Günter M. Ziegler, in Handbook of Discrete and Computational Geometry, 2017 CRC link.

Although the isotopy property holds for $3$-polytopes (Steinitz's Theorem), it was proved by Richter-Gebert that it fails in dimension $4$. This is his "Universality Theorem."

I believe your question asks about isotopy:

Isotopy property: A combinatorial structure (such as a combinatorial type of polytope) has the isotopy property if any two realizations with the same orientation can be deformed into each other by a continuous deformation that maintains the combinatorial type. Equivalently, the isotopy property holds for a combinatorial structure if and only if its realization space is connected.

This definition is quoted from "Basic Properties of Convex Polytopes" by Martin Henk, Jürgen Richter-Gebert, and Günter M. Ziegler, in Handbook of Discrete and Computational Geometry, 2017. CRC link.

Although the isotopy property holds for $3$-polytopes (Steinitz's Theorem), it was proved by Richter-Gebert that it fails (quite badly) in dimension $4$. This is his "Universality Theorem."

I believe your question asks about isotopy:

Isotopy property: A combinatorial structure (such as a combinatorial type of polytope) has the isotopy property if any two realizations with the same orientation can be deformed into each other by a continuous deformation that maintains the combinatorial type. Equivalently, the isotopy property holds for a combinatorial structure if and only if its realization space is connected.

This definition is quoted from "Basic Properties of Convex Polytopes" by Martin Henk, Jürgen Richter-Gebert, and Günter M. Ziegler, in Handbook of Discrete and Computational Geometry, 2017 CRC link.

It was proved by Richter-Gebert (Universality Theorem) that the isotopy property fails in dimension $4$, although it holds for $3$-polytopes (Steinitz's Theorem).

I believe your question asks about isotopy:

Isotopy property: A combinatorial structure (such as a combinatorial type of polytope) has the isotopy property if any two realizations with the same orientation can be deformed into each other by a continuous deformation that maintains the combinatorial type. Equivalently, the isotopy property holds for a combinatorial structure if and only if its realization space is connected.

This definition is quoted from "Basic Properties of Convex Polytopes" by Martin Henk, Jürgen Richter-Gebert, and Günter M. Ziegler, in Handbook of Discrete and Computational Geometry, 2017 CRC link.

Although the isotopy property holds for $3$-polytopes (Steinitz's Theorem), it was proved by Richter-Gebert that it fails in dimension $4$. This is his "Universality Theorem."