Here is a model of the Ka'bah including a representation of its courtyard and a plan of the Masjid Al-Haram. It can be cut out with flaps or used as a guide for a more elaborate model using cloth, gold stickers etc..
Ka'bah means cube and the building in Makkah is cube shaped with an indented flat roof with silvery tiles on top. The roof is held up with two columns inside. There is a staircase to the roof.
It is built of mud brick and tree trunks. A meteorite called the Black Stone is set into a vulva shaped silver sheet container extended along the bulbous sides as it juts out at the corner, almost set like an eye.
From a non-Muslim point of view the Black Stone is almost a vestage of Paganism being at the centre of the direction of world-wide prayer. Muslims instead regard it as a highly venerated object because of the belief that Abraham handled this very meteorite and indeed his son found it for Abraham to stand on in order to build the first Ka'bah. Non Muslims would be puzzled why Abraham, already a very mysterious figure lost in time, would venture into Arabia. The Kab'ah has been rebuilt many times but, Muslims say, the Black Stone has been continuoously present. Muhammad removed pagan symbols from the Kab'ah and set the Black Stone.
The Ka'bah has needed protection and this is why it has been covered with a cloth. Since the growth of the Muslim community, thick black cloths embroidered with Arabic calligraphy drawing from Qur'anic verses have been used, usually a new one each year. The cover is changed so frequently because of the sun. At one time the covers came from Egypt but now they come from within Saudi Arabia.
Model makers may want to create a tile effect circular courtyard for it to stand on. There is a low semi-circular platform and a strong boundary line before the circular tiled courtyard. This is where pilgrims circle the Ka'bah seven times on two occasions during the Hajj.
The Ka'bah and area for pilgrims is part of the large and thoroughly rebuilt Masjid Al-Haram. This plan shows how the Ka'bah sits within the mosque. The long arm is the travellator between the two hills of Marwah to the north and Safa at the south (closer to the body of the mosque); the ladies areas are to the east of the travellator.
Original idea and some basic information from:
Al-Gailani, N., Smith, C. (2002), The Islamic Year: Surahs, Stories and Celebrations, Stroud: Hawthorn Press.