a.k.a. Rounded Halpern-Meier Pyramid
Made by Mefferts, 2010.
(plastic, 4 inches;
left: fluorescence labels - back is orange, bottom is green;
right: Cube Smith labels - back is green, bottom is blue)

This puzzle is like the Pyraminx, except it does not have the tips but does have face centers (triangles). We use the same notation for solving, less any reference to tips.

Notation: There are 4 corners and 6 edges. Holding the puzzle with one of the faces towards you, clockwise and counterclockwise rotations of the top, lower left, and lower right corners are denoted by T+, T-, L+, L-, R+, and R-; 3 means do it three times.

Solution:

1. Solve the corners and edges with a solution for the Pyraminx.
   
   Note: Without tips to keep you oriented, it can help to determine the colors of the sides once at the start, and then for the remainder of the solving, keep the puzzle in a fixed orientation with the same side facing down and the same side facing you.
   
   
2. Use the following transformation, given on Jaap's Page, to fix the centers (it exchanges the front and bottom triangles and the left and right triangles):

( R   T   R-   T- ) ³

Further Reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/PyraminxJing.htm