The precise teapot form called "蝴蝶汉瓦" is not a standard, widely documented category in the literature I have access to, so the name appears to combine two motifs—蝴蝶 (butterfly) and 汉瓦 (Han [dynasty] roof tile) —rather than refer to a single canonical historical model. Briefly: many Chinese teapots and vessels take their names from animals, architectural elements, or everyday objects, and potters have long combined decorative motifs in imaginative, regionally specific ways.

Historical context: from the Ming and especially the Qing periods onward, Chinese ceramic and Yixing clay workshops produced playful, sculptural teapots shaped as animals, plants, and architectural forms. The butterfly is a recurring decorative and symbolic motif in Chinese art (love, joy, longevity), and references to Han-dynasty tiles or tile patterns are also used decoratively to evoke antiquity and architectural form. Combining these elements would fit into a broader tradition of novelty and revivalist teapots made for aesthetic and collectible use rather than strict utilitarian prototypes.

Shape note: a "butterfly–Han-tile" teapot would likely pair a low, slightly ridged or tiled body (suggesting a roof tile profile) with butterfly accents — relief wings, a butterfly-shaped handle or lid finial — resulting in a compact, sculptural teapot emphasizing form and surface decoration as much as pouring performance.
Wood-fired handmade Yixing teapot made from Duanni clay sourced from the original Huanglongshan mine. Xu Shun Wei.