Although collaborative practices between cyber organizations are well documented, managing activities within these organizations is still challenging as cyber operators tasks are very demanding and usually done individually. As human factors studies in cyber environments are still difficult to perform, tools and collaborative practices are evolving slowly and training is always required to increase teamwork efficiency. Contrary to other research fields, cyber security is not harnessing yet the capabilities of Collaborative Virtual Environments (CVE) which can be used both for immersive and interactive data visualization and serious gaming for training. In order to tackle cyber security teamwork issues, we propose a 3D CVE called the 3D Cyber Common Operational Picture, which aims at taking advantage of CVE practices to enhance cyber collaborative activities. Based on four Security Operations Centers (SOCs) visits we have made in different organizations, we have designed a cyber collaborative activity model which has been used as a reference to design our 3D CyberCOP platform features, such as asymetrical collaboration, mutual awareness and roles specialization. Our approach can be adapted to several use cases, and we are currently developing a cyber incident analysis scenario based on an event-driven architecture, as a proof of concept.