From the Super Mario Wiki
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Semi-Solid Platforms are platforms found throughout the Super Mario series that the player can jump through from the bottom. They have a different design in each installment, first appearing in Super Mario Bros. 2. Another kind of Semi-Solid Platform is the Mushroom Platform.
Super Mario series
Super Mario Bros. 2
Super Mario Bros. 3
White platforms have the special property of allowing Mario to fall into the background, behind most objects, by crouching on them for an extended time. If, as is possible in World 1-3, the goal area is reached in this state, Mario is transported to a special Toad House to receive a Warp Whistle.
Super Mario World
New Super Mario Bros. series
Semi-Solid Platforms appeared in New Super Mario Bros., New Super Mario Bros. Wii, New Super Mario Bros. 2, and New Super Mario Bros. U. While they have new, varying designs throughout the series, the most common design in all games is that consisted of small blocks placed next to each other. Certain Semi-Solid Platforms in New Super Mario Bros. 2 are based off their design from Super Mario Bros. 3.
Super Mario Maker
Semi-Solid Platforms appear as tools in Super Mario Maker. In Create mode, they can be shaken into three different designs. In the Super Mario Bros. style, Semi-Solid Platforms take their default design from the otherwise solid, tree-like platforms from that game.
If the player were to crouch on the white platforms for long enough, Mario will hop slightly, referencing the special property of the white platform from Super Mario Bros. 3, though not letting Mario drop behind the platform.
Super Smash Bros. for Nintendo 3DS / Wii U
Semi-Solid Platforms also appear in the stage Mushroom Kingdom U where they, like the stage itself, use their design from New Super Mario Bros. U. Like all soft platforms in the Super Smash Bros. series, the player can fall through the Semi-Solid Platform by tapping .