Can You Protect an Egg from a 40 ft Drop Using Only Straws and Rubber Bands?

[Condensate]

Homework Statement

Problem:
Create a means for the egg to land on an uneven dirt surface from a great height without breaking.

Restrictions:
No parachutes (or wings, or any other velocity-slowing addition,) packing materials/padding, balloons, or thick liquid substances.
The project must not exceed the dimensions of 4x4x6 inches.

Purpose:
The project is focused on the concept of impulse on the egg.

Homework Equations

I don't know the exact height it is dropped from, but I'd estimate it to be about 40 ft. The egg itself weighs about 70 g.

p=mv
Ft=m▲v=J=▲p
v_f²=v_o²+2g▲y

The Attempt at a Solution

These are my two attempts at creating a chamber for the egg to take refuge in:

1. Materials: Cardboard, tape, Plastic Wrap (blue)
I created a 4x4x6 box that held an irregular box with lots of space in it. Beams of cardboard supported the structure of the box and together with the plastic wrap held the smaller box in place. The design was a mess, and the egg was destroyed.

2. Materials: Cardboard, Rubber Bands, Tape
Again created a 4x4x6 box (enclosed on every side) to hold a smaller box (now with tape and the sides of the box snugly hugging the egg) that was suspended by 6 rubber bands. Took a day or so to make. The egg was in a better shape than before when dropped, but it was still smashed.

3. (?) Materials: Straws, Rubber Balls, Rubber Bands
I haven't made this yet, but I'm thinking about trying a a network of straws in the fashion of a triangular pyramid. Are the rubber balls a bad idea?

I would be very grateful if someone suggests something. I'm basically thinking of a way to increase the time the the impulse works on the egg in order for the force to be reduced to a manageable level. A way to distribute the force around the surface of the egg would also work well (cereal would definitely work, but I'm not sure if that would fall under the category of "packing materials," so I'm hesitant about that.) It's due tomorrow. Once again, any help is appreciated!
Thank you!

 

[Chronos]

A symmetrical shape is preferred with the egg centered in the enclosure. I would use plastic straws, creating a series of interlinked pyramids forming a polyhedral outer surface. Center and secure egg in enclosure. This provides maximum allowable distance between egg and that big chicken nest in the sky. Heat fusing the joints is generally better than glue.

 

[Condensate]

Thank you so much, Chronos!
I'm using duct tape for the joints (been working on a straw frame for about half an hour.)