Final answer:
Among the options provided, erysipelas is a type of cellulitis that presents as a large, intensely inflamed patch of skin and is often caused by Streptococcus pyogenes.
Step-by-step explanation:
The type of cellulitis among the options provided is e) erysipelas. Cellulitis is an infection that develops in the dermis or hypodermis, presenting as a reddened area of skin that is warm to the touch and painful. The causative agent is often Streptococcus pyogenes, which may breach the skin through a cut or abrasion.
Streptococcus pyogenes can also cause erysipelas, presenting as a large, intensely inflamed patch of skin involving the dermis, often on the legs or face. Other conditions mentioned, such as impetigo and acne vulgaris, are different types of skin infections.