How to list an entries selected nested categories?
The final solution I got to work:

{% set cats = entry.categories %}
{% for cat in cats %}
    {% if cat.slug == 'secondlevel1' or cat.slug == 'secondlevel2' %}
        {% set catChildren = cats.descendantOf(cat.id).descendantDist('1') %}
        {% if catChildren | length %}
            {% for childCat in catChildren %}
                {% set image = childCat.buildingBlockIcon.first() %}
                    {% if image %}
                        &lt;img alt="{{ childCat.title }}" src="{{ image.url }}" /&gt;
                    {% endif %}
            {% endfor %}
        {% endif %}
    {% endif %}
{% endfor %}