Hey! This isn't my area of expertise but I was able to do a little research into the topic. I've tried to give a brief introduction below, so hope it helps.

Geometric Art in Islam

Geometry has long held a vaunted place in Islamic art, with treatises being written on the subject as early as the 9th century. The actual use of geometry in art pre-dated those works, and can be seen in structures across the middle east: the Dome of the Rock and the Great Mosque of Damascus being two such examples.

Originally, geometric patterns were not unique to the Islamic world. The Zoroastrian Sassanid Empire and Christian Byzantine Empire both used similar motifs. The Great Mosque of Damascus was actually adopted from a Christian Temple that made use of floral motifs to represent the gardens of the city. So why do these patterns just scream "Islamic Art" today?

For one, there is some religious significance to the use of repeating geometric shapes that contributed to their longevity. One paper I read on this described the repetition of simple geometric patterns using a Sufi saying: "endless multiplicity of creation issued from single: multiplicity in the unity." Simple shapes such as circles were seen to represent the Unity of Islam and the Oneness of God. The linking of more complex shapes, made possible by mathematical development in the Islamic world, likewise demonstrated the this "infinitness" of Islam. Certain shapes then had their own, unique meanings. For example, the eight-pointed star (Rub' al-Hizb, seen here on a medieval Moroccan flag) comes from a tool used to assist in the memorization of the Qur'an.

I also want to note the additional impact of religious trends away from depicting human and animal forms. While there isn't a clear-cut, Qur'anic prohibition, various hadīths led to a desire to avoid committing shirk (assigning partners to God and thus denying his unity) that may have resulted from e.g. sculptures or paintings of people. I wrote more on this topic in a previous answer here. In lieu of the representing people, many Islamic artists used geometric motifs like those you linked.

Finally, I did some research into the 10-pointed start in the center of the image you linked and unfortunately couldn't find too much. From what I found, the earliest 10-pointed geometric patterns date back to roughly the 11th century. However, I couldn't find a definitive meaning for the 10-pointed star itself, beyond that it may arise from the combination of 2 pentagons (which have their own meaning in Islam. Think of the 5 Pillars of Islam, for example).

As a side note, two examples of buildings with 10-pointed stars that I saw mentioned in another paper were the North Dome Chamber of the Masjid-i Jami' at Isfahan and the Victory Tower of Masud III at Ghazni in Afghanistan. I reverse image searched your photo and didn't find it anywhere. Is there any chance it comes from the Iran/Afghanistan region?

Sources

• Evolution of Islamic geometric patterns by Yahya Abdullahi and Mohamed Rashid Bin Embi

• Islamic Star Patterns by A.J. Lee

• Study of Sacred Geometry in Islamic Architecture by Nazli Hesar, Nasim Kalantari, and Mortaza Ahmadi.