You can use the following geometries at the moment.
As described in this tutorial, there are two ways to specify a geometry. One is fully customizable the other is easy but less customizable. For example, a box geometry is used in the following two ways.
<three-canvas width="200" height="200" antialias="true" clear-color="#000000" default-light="true">
<three-camera position="0,0,8" look-at="0,0,0" controls="orbit"></three-camera>
<three-mesh>
<three-material color="#ffffff" map="../images/earth.jpg"></three-material>
<three-box-geometry width="1" height="1" depth="1"></three-box-geometry>
</three-mesh>
</three-canvas><three-canvas width="200" height="200" antialias="true" clear-color="#000000" default-light="true">
<three-camera position="0,0,8" look-at="0,0,0" controls="orbit"></three-camera>
<three-box width="1" height="1" depth="1" color="#ffffff" map="../images/earth.jpg"></three-box>
</three-canvas>