T. fluminensis is a perennial ground cover that spreads along the ground with soft, hairless stems and leaves. The fleshy stems root at any node that is on the surface. The plant has oval, dark-green leaves with pointed tips that are shiny, smooth and slightly fleshy about 1.25 - 2.5 inches long. The flowers are white with three petals and approx. 0.5 - 1 inch in diameter. They are produced in small clusters in summer but do not produce seeds.